Inclusion Criteria

          -  Histologically or cytologically confirmed diagnosis of locally-advanced unresectable
             or metastatic solid tumor, including primary brain tumors

          -  Participants with disease types other than breast cancer, biliary tract cancer,
             non-squamous NSCLC, and cervical cancer: Disease progression on or after the most
             recent systemic therapy for locally-advanced unresectable or metastatic disease

          -  Participants with any breast cancer subtype:

               -  Must have HER2-mutated disease which does not display HER2
                  overexpression/amplification

               -  Must have progressed on or after ≥1 prior line of treatment (chemotherapy,
                  endocrine therapy, or targeted therapy) for locally-advanced unresectable or
                  metastatic breast cancer

               -  Participants with metastatic HR+ HER2-mutated disease must have received a prior
                  CDK4/6 inhibitor in the metastatic setting.

          -  Participants with biliary tract cancer: must have completed ≥1 prior line of treatment
             (chemotherapy, endocrine therapy, or targeted therapy)

          -  Participants with non-squamous NSCLC: has relapsed from or is refractory to standard
             treatment or for which no standard treatment is available

          -  Participants with cervical cancer:

               -  Participants with metastatic cervical cancer must have progressed on or after ≥1
                  prior line of systemic therapy in the metastatic setting.

               -  Participants with locally advanced unresectable cervical cancer must have
                  progressed on or after ≥1 prior lines of systemic therapy.

          -  Disease demonstrating HER2 alterations (overexpression/amplification or HER2
             activating mutations), as determined by local or central testing processed in a
             Clinical Laboratory Improvement Amendments (CLIA)- or International Organization for
             Standardization (ISO) accredited laboratory, according to one of the following:

          -  HER2 overexpression/amplification from fresh or archival tumor tissue or blood

          -  Known activating HER2 mutations detected in fresh or archival tumor tissue or blood

          -  Have measurable disease per RECIST v1.1 criteria according to investigator assessment

          -  Have Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1

        Exclusion Criteria

          -  Participants with breast cancer, GEC, or CRC whose disease shows HER2
             amplification/overexpression.

          -  Previous treatment with HER2-directed therapy; participants with uterine serous
             carcinoma may have received prior trastuzumab

          -  Known hypersensitivity to any component of the drug formulation of tucatinib or
             trastuzumab (drug substance, excipients, murine proteins), or any component of the
             drug formulation of fulvestrant in participants with HR+ HER2-mutated breast cancer

          -  History of exposure to a 360 mg/m² doxorubicin-equivalent or >720 mg/m^2
             epirubicin-equivalent cumulative dose of anthracyclines

          -  Treatment with any systemic anti-cancer therapy, radiation therapy, or experimental
             agent within ≤3 weeks of first dose of study treatment or are currently participating
             in another interventional clinical trial.

        There are additional inclusion and exclusion criteria. The study center will determine if
        criteria for participation are met.