ELVN-002 With Trastuzumab +/- Chemotherapy in HER2+ Solid Tumors, Colorectal and Breast Cancer

Inclusion Criteria: * Pathologically or histologically documented solid tumor. * Locally advanced or relapsed/refractory disease or unresectable metastatic disease. * HER2-positive disease based on the following local testing: * Colorectal cancer: IHC3+, IHC2+/ISH+, NGS amplification by tissue (no RAS or BRAF mutation allowed) * Breast cancer: IHC3+ or IHC2+/ISH+ by tissue * Gastric cancer: IHC3+ or IHC2+/ISH+ by tissue * Other cancers: IHC3+, IHC2+/ISH+, NGS amplification by tissue or ctDNA * Prior therapies for Part 1 (Dose Escalation ELVN-002 + trastuzumab): * Colorectal cancer: treated with prior fluoropyrimidine, oxaliplatin, irinotecan-based regimens, anti-epidermal growth factor receptor (EGFR) treatment (if clinically indicated), anti-vascular endothelial growth factor (VEGF) treatment (if clinically indicated), and an anti-programmed death ligand 1 (PD-(L)-1) treatment (if the tumor is microsatellite instability (MSI)-high/deficient mismatch repair (dMMR) * Breast cancer: treated with prior taxane, pertuzumab, trastuzumab, and fam-trastuzumab deruxtecan (T-DXd) if available and appropriate based on local standard of care and investigator's assessment * Gastric cancer: treated with trastuzumab/platinum fluorouracil containing regimen and T-DXd. * Other cancers: progressed during or after ≥ 1 prior line of systemic therapy for locally advanced unresectable or metastatic disease * Prior HER2 targeted therapy is allowed * Prior therapies for Part 2 (Phase 1a Dose Escalation ELVN-002 + trastuzumab + chemotherapy): * Colorectal cancer: candidate for CAPEOX (capecitabine and oxaliplatin) or mFOLFOX6 (5-FU, LCV and oxaliplatin), and treated, if clinically indicated, with an anti-programmed death ligand 1 (PD-(L)-1) treatment (if the tumor is microsatellite instability (MSI)-high/deficient mismatch repair (dMMR). Prior HER2 targeted therapy is allowed. * Breast cancer: candidate for capecitabine, paclitaxel or eribulin, and treated with prior taxane, pertuzumab, trastuzumab, and T-DXd, if available and appropriate, based on local standard of care and investigator's assessment. No prior HER2 targeted tyrosine kinase inhibitor therapy (antibody-drug conjugates and antibodies are allowed), no prior capecitabine (for the capecitabine cohort), no prior eribulin (for the eribulin cohort), and no taxane as immediate prior therapy (paclitaxel cohort). * Prior therapies for Part 3 (Phase 1b Dose Expansion ELVN-002 + trastuzumab): * Colorectal cancer: treated with prior fluoropyrimidine, oxaliplatin, irinotecan-based regimens, anti-epidermal growth factor receptor (EGFR) treatment (if clinically indicated), anti-vascular endothelial growth factor (VEGF) treatment (if clinically indicated), and an anti-programmed death ligand 1 (PD-(L)-1) treatment if the tumor is microsatellite instability (MSI)-high/deficient mismatch repair (dMMR). No prior HER2 targeted therapy. * Breast cancer: treated with prior taxane, pertuzumab, trastuzumab, and T-DXd if available and appropriate based on local standard of care and investigator's assessment. No prior HER2 targeted tyrosine kinase inhibitor therapy (antibody-drug conjugates and antibodies are allowed). * Gastric cancer: treated with prior trastuzumab/platinum fluorouracil containing regimen and T-DXd. No prior HER2 targeted therapy. * Other cancers: Progressed during or after ≥ 1 prior line of systemic therapy for locally advanced unresectable or metastatic disease. No prior HER2 targeted therapy. * Prior therapies for Part 4 (Phase 1b Dose Expansion ELVN-002 + trastuzumab + chemotherapy): \* Colorectal cancer: candidate for CAPEOX or mFOLFOX6 and not a candidate for first-line anti-programmed death ligand 1 (PD-(L)-1) treatment (if the tumor is microsatellite instability (MSI)-high/deficient mismatch repair (dMMR). No prior therapy for metastatic disease (1 cycle of mFOLFOX6 or 1 cycle of CAPEOX allowed). No prior HER2 targeted therapy. * At least 1 measurable lesion based on RECIST v 1.1 within 6 weeks before the first dose of ELVN-002 (Part 3 and Part 4 only; Phase 1b Dose Expansion cohorts) * Eastern Cooperative Oncology Group (ECOG) performance status of 0-1 * Adequate hematological, hepatic, renal, and cardiac function Exclusion Criteria: * Treatment with anticancer therapy within a specific time before the first dose: * Chemotherapy (including ADC) ≤ 3 weeks * Immunotherapy ≤ 4 weeks * Hormonal therapy ≤ 2 weeks * TKI ≤ 2 weeks * Any experimental therapy ≤ 3 weeks or 5 half-lives, whichever is longer * Radiotherapy-wide therapy ≤ 3 weeks * Radiotherapy limited field (including stereotactic brain) ≤ 2 weeks * Antibody ≤ 3 weeks * Any brain lesion requiring immediate local therapy * Ongoing use of corticosteroids for central nervous system (CNS) symptoms at a dose of \> 2 mg daily of dexamethasone (or equivalent) * Leptomeningeal disease * Uncontrolled seizures * Participants for any chemotherapy cohort: ongoing Grade 2 or higher neuropathy of any cause * Inability to swallow pills or any significant gastrointestinal disease that would preclude adequate oral absorption of medications. * Ongoing adverse effects from prior treatment \> CTCAE Grade 1 except for Grade 2 alopecia * Corrected QT interval (QTc) of \>470 milliseconds (ms) for females or \>450 ms for males