Inclusion Criteria:

          -  Patients must have histologically or cytologically confirmed solid organ malignancy

          -  Patients enrolled in the expansion cohort must have histologically or cytologically
             confirmed squamous non-small cell lung cancer (NSCLC), breast or pancreaticobiliary
             tract cancer

          -  Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2

          -  Patients must have measurable disease, defined as at least one lesion that can be
             accurately measured in at least one dimension (longest diameter to be recorded for
             non-nodal lesions and short axis for nodal lesions) as ≥ 20 mm (≥ 2 cm) with
             conventional techniques or as ≥ 10 mm (≥ 1 cm) with spiral computed tomography (CT)
             scan, magnetic resonance imaging (MRI), or calipers by clinical exam

          -  Leukocytes ≥ 3,000/mL

          -  Absolute neutrophil count ≥ 1,500/mL

          -  Platelets ≥ 100,000/mL

          -  Hemoglobin ≥ 10 g/dL

          -  Total bilirubin ≤ 1.5 × institutional upper limit of normal (except for patients with
             Gilbert disease)

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase [SGOT])/
             alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) ≤ 2.5 ×
             institutional upper limit of normal (up to 5 X upper limit of normal [ULN] for
             patients with liver metastasis)

          -  Creatinine within normal institutional limits OR creatinine clearance ≥ 60 mL/min/1.73
             m² for patients with creatinine levels above institutional normal

          -  Women of child-bearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control; abstinence) prior to study entry and for
             the duration of study participation; should a woman become pregnant or suspect she is
             pregnant while she or her partner is participating in this study, she should inform
             her treating physician immediately; men treated or enrolled on this protocol must also
             agree to use adequate contraception prior to the study, for the duration of study
             participation, and for 6 months after completion of study drug administration

          -  Ability to understand and the willingness to sign a written informed consent document

        Exclusion Criteria:

          -  Patients who have had cytotoxic anticancer chemotherapy or immune checkpoint inhibitor
             within 4 weeks (6 weeks for nitrosoureas or mitomycin C) or palliative radiation
             within 2 weeks (stereotactic radiation therapy [SRS] for brain metastasis within 48
             hours) prior to entering the study or those who have not recovered from adverse events
             due to agents administered more than 4 weeks earlier

          -  Patients receiving cytotoxic agent as immunomodulatory therapy for a non neoplastic
             indication (e.g. methotrexate for rheumatoid arthritis) and who are unable to
             discontinue such agents within 2 weeks prior to starting treatment

          -  Oral targeted therapy within five days or five half-lives, whichever is longer, prior
             to initiating protocol therapy treatment

          -  Patients who are receiving any other investigational agents

          -  Use of strong cytochrome P450, family 3, subfamily A (CYP3A) inhibitors and inducers

          -  Patients with symptomatic uncontrolled brain metastases are excluded; (patients with
             stable treated or asymptomatic untreated brain metastasis not requiring
             glucocorticoids are allowed)

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to palbociclib, carboplatin or cisplatin

          -  Concurrent administration of strong inducers and inhibitors of CYP3A enzyme or CYP3A
             substrates with narrow therapeutic window

          -  Uncontrolled intercurrent illness including, but not limited to:

               -  Ongoing or active infection requiring intravenous antibiotics at the time of
                  treatment initiation

               -  Symptomatic congestive heart failure (requiring hospital stay within the last 6
                  months)

               -  Myocardial infarction within the last 6 months

               -  Unstable angina pectoris, cardiac arrhythmia

               -  Psychiatric illness

          -  Social situations or circumstances that would limit compliance with study requirements

          -  Pregnant women are excluded from this study; breastfeeding should be discontinued if
             the mother is treated with palbociclib

          -  Human immunodeficiency virus (HIV)-positive patients on combination antiretroviral
             therapy are ineligible