Palbociclib With Cisplatin or Carboplatin in Advanced Solid Tumors

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