Inclusion criteria:

          1. Patient has an advanced, histologically-proven solid tumor of one of the following
             types, treated with at least one line of systemic therapy, and for which approved
             therapies have been exhausted or for which the Investigator considers the patient
             ineligible or intolerant of other forms of treatment: Colorectal, Ovarian,
             Endometrial, Gastric, Pancreatic, Anal, Cervical, Squamous cell cancer of the head and
             neck, Mesothelioma, Prostate, Non-small cell lung cancer, Melanoma,
             Urothelial/bladder, Microsatellite instability high tumors of any type, Cutaneous
             squamous cell, Breast,

          2. Patients have to be willing to comply with study procedures

          3. ≥18 years of age

          4. Mentally competent, able to understand and willing to sign the ICF

          5. Eastern Cooperative Oncology Group performance status (ECOG; PS) ≤1

          6. Anticipated life expectancy ≥12 weeks by Investigator judgment

          7. The disease is measurable according to Response Evaluation Criteria in Solid Tumors
             (RECIST) v1.1 criteria

          8. Mandatory paired pre- and on-treatment biopsies - preferably from the same lesion -
             are required as follows:

               1. At least 1 tumor lesion ≥10 mm amenable to percutaneous biopsy other than the
                  target lesion used to follow response as defined by RECIST v1.1

               2. For cutaneous or subcutaneous lesions, tumors should be ≥ 5mm in diameter
                  amenable to paired biopsy by excisional or punch biopsies without unacceptable
                  risk of a major procedural complication

               3. For core needle biopsy specimens three to six 18 gauge cores should be collected.
                  If more than 1 biopsy is planned to be taken from one lesion, the lesion should
                  be large enough to permit successive biopsies preferably ≥1 cm apart.

          9. At least 4 weeks must have elapsed from any prior major surgery. The following
             procedures are not considered major surgical procedure:

               1. Obtaining the pre-treatment biopsy as per protocol requirements

               2. Placement of a port for central venous access

               3. Needle, punch or excisional biopsy of a clinically or radiographically detected
                  lesion

         10. Laboratory values at screening must be:

             a. Adequate hematology: i. platelet count ≥100,000 cells/mm3 ii. absolute neutrophil
             count ≥1,000 cells/mm3 iii. hemoglobin ≥9 g/dL b. Serum creatinine ≤1.5 x upper limit
             of normal (ULN) or creatinine clearance ≥50 mL/min on the basis of CKD-EPI (Chronic
             Kidney Disease Epidemiology Collaboration), Cockcroft-Gault, or Modification of Diet
             in Renal Disease (MDRD) glomerular filtration rate estimation c. Adequate coagulation:
             iv. INR must be <1.5, unless on therapeutic anticoagulants v. PT and activated partial
             thromboplastin time (aPTT) ≤1.6 x ULN unless therapeutically warranted d. Aspartate
             aminotransferase (AST) and alanine aminotransferase (ALT) <3x ULN e. Bilirubin <1.5 x
             ULN, except for patients with a known familial hyperbilirubinemia (such as e.g.,
             Gilbert syndrome). For patients with documented Gilbert's syndrome
             (Gilbert-Meulengracht syndrome) total bilirubin <3 x ULN is acceptable) f. Potassium,
             calcium, and magnesium that are >0.9 of LLN and ≤1.1 of ULN. Supplementation is
             allowed for potassium, calcium and magnesium to reach these values

         11. A woman of childbearing potential (WOCBP) should only be included after a confirmed
             menstrual period and a negative serum pregnancy test at Screening.

             a. Where ovarian activity is being suppressed by chemotherapy, confirmation of
             non-pregnancy by menstrual period is not required

         12. A female patient is eligible to participate if she is not pregnant, not breastfeeding
             (for 12 months following last dose of rituximab), and at least one of the following
             conditions applies:

               1. Not a woman of child bearing potential (WOCBP)

               2. A WOCBP who agrees to follow the contraceptive guidance during the treatment
                  period and for at least 3 months after the last dose of MP0310 and 12 months
                  after the last dose of rituximab, whichever is longer.

         13. Men who are not surgically sterilized (and with appropriate post vasectomy
             documentation of the absence of sperm in the ejaculate) and who are partners of WOCBP
             must be willing to use adequate contraception as detailed in Section 15.7 from the
             Screening visit, during the treatment period, and for at least 3 months after the last
             MP0310 IMP administration and refrain from donating sperm during this period.

         14. Covered by healthcare insurance (if applicable, in accordance with local regulations)

        Exclusion criteria

          1. Known hypersensitivity to the following excipients that are used for formulation of
             MP0310:

             a. L-histidine, L-histidine hydrochloride, D-mannitol and polysorbate 20

          2. Patients with autoimmune diseases, except auto-immune endocrinopathies that are stable
             with hormone replacement therapy

          3. Patients with inflammatory diseases such as arthritis, colitis, liver fibrosis,
             cirrhosis, interstitial fibrosis, or COPD (chronic obstructive pulmonary disease; that
             may have elevated tissue FAP expression) unless approved after consultation by the
             Medical Monitor (MM).

          4. Concurrent enrollment in another clinical study, unless it is an observational (non
             interventional) clinical study for the duration of this study or the follow-up period
             of an interventional study

          5. Patient was previously treated in this study

          6. Serious illness or concomitant non-oncological disease considered by the Investigator
             to be incompatible with participating in the protocol

          7. Bisphosphonate therapy for symptomatic hypercalcemia

             a. Patients on stable dose of bisphosphonate therapy or receptor activator of nuclear
             kappa-B ligand (RANKL)-therapy for more than 8 weeks prior to first scheduled dose of
             MP0310 for other reasons (e.g., bone metastasis or osteoporosis) are allowed

          8. Use of an investigational agent within the past 4 weeks before first MP0310 IMP
             administration in this study

          9. Any anti-cancer therapy, including chemotherapy, hormonal therapy, or radiotherapy,
             within 3 weeks prior to first MP0310 IMP administration; however, the following are
             allowed:

               1. Hormonal therapy with gonadotropin-releasing hormone (GnRH) agonists or
                  antagonists for prostate cancer

               2. Hormone-replacement therapy or oral contraceptives

               3. Palliative radiotherapy for bone metastases 2 weeks prior to first MP0310 IMP
                  administration

         10. Corticosteroid use exceeding 10 mg/day prednisone or equivalent

         11. Left ventricular ejection fraction of <50% on echocardiographic exam or multigated
             acquisition (MUGA) scan at screening

         12. Any history or evidence of clinically significant cardiovascular disease defined as at
             least one of the following criteria:

               1. Evidence of poorly controlled arterial hypertension (systolic blood pressure >160
                  mmHg or diastolic blood pressure >100 mmHg)

               2. Myocardial infarction or instable angina pectoris within the previous 6 months

               3. Documented history of congestive heart failure of New York Heart Association >2
                  criteria

               4. Any cardiac arrhythmia that is not well controlled

               5. QT corrected (QTc) prolongation > Grade 1 (>480 ms) at screening measured on 2
                  separate electrocardiograms (ECGs) at least 10 minutes apart

               6. Clinically significant valvular heart disease

         13. Severe dyspnea, pulmonary dysfunction, or need for continuous supportive oxygen
             inhalation

         14. Arterial thromboembolic event, stroke, or transient ischemia attack within the past 12
             months

         15. Patients with known central nervous system (CNS) metastasis that are either untreated
             or are treated but are associated with clinical symptoms (e.g., headache,
             convulsions). Patients with CNS metastasis that have been treated with radiotherapy
             and/or surgery are eligible if they are clinically without symptoms for at least 6
             weeks; if under treatment with corticosteroids (not exceeding 10 mg/day prednisone or
             equivalent) and/or anticonvulsive agents patients must be on a stable dose for at
             least two weeks.

         16. Any active uncontrolled bleeding, or a bleeding diathesis

         17. Therapy for active infection needs to be completed at least 7 days prior to the start
             of therapy

         18. Patients with a known positivity for human immunodeficiency virus (HIV)

         19. Patients with active hepatitis B (chronic or acute; HBV) defined as having a positive
             hepatitis B surface antigen (HbsAg) test at screening. Patients with past or resolved
             HBV infection (defined as having a negative HbsAg test and a positive antibody to
             hepatitis B core antigen antibody test) are eligible.

         20. Patients with active hepatitis C (HCV) infection defined as having a positive HCV
             antibody test followed by a positive HCV ribonucleic acid (RNA) test at screening. The
             HCV RNA test will be performed only for patients who have a positive HCV antibody
             test. Patients who are positive for HCV antibody are eligible only if polymerase chain
             reaction (PCR) is negative for HCV RNA.

         21. Serious or non-healing wound, skin ulcer, or non-healing bone fracture

         22. Abdominal fistula, gastrointestinal perforation, or intra-abdominal abscess within the
             past 6 months

         23. Albumin <2.8 g/dL or <28 g/L, and without albumin transfusion for ≥7 days prior to
             screening

         24. Unwilling or unable to follow protocol requirements

         25. Any live virus vaccine within 30 days prior to the start of therapy

         26. Has had an allogenic tissue/solid organ transplant

         27. History of another primary malignancy except for:

               1. Malignancy treated with curative intent and with no known active disease ≥2 years
                  before the first dose of investigational product and of relatively low potential
                  risk for recurrence

               2. Adequately treated non-melanoma skin cancer or lentigo maligna without evidence
                  of disease

               3. Adequately treated carcinoma in situ without evidence of disease

               4. Cancer patients with incidental histologic findings of prostate cancer that, in
                  the opinion of the Investigator, is not deemed to require active therapy (e.g.,
                  incidental prostate cancer identified following cystoprostatectomy that is
                  tumor/node/metastasis Stage ≤ pT2N0) may be enrolled, pending discussion and
                  approval by the MM

         28. Male or female patients of reproductive potential who are not willing to employ
             adequate contraception from screening to at least 3 months after the last MP0310 IMP
             administration

         29. Any condition that, in the opinion of the Investigator, would interfere with
             evaluation of the MP0310 IMP or interpretation of the patient's safety or study
             results

         30. Patient deprived of liberty by a judicial or administrative decision, patient admitted
             to a social institution or who is under a measure of legal protection, patient
             hospitalized without consent or who is in an emergency situation

         31. Known hypersensitivity or allergy to murine products or any excipients of rituximab
             (Part C only)

         32. Active, severe infections and/or severely immunocompromised state

         33. Contraindication against mandatory prophylactic premedication