This is an open-label study. This means that people in this study and clinic staff will know that they will receive ASP3082. The study aims to check how safe and well-tolerated ASP3082 is for people with advanced solid tumors that have a specific mutation called KRAS G12D.

This study will be in 2 parts.

In Part 1, different small groups of people will receive lower to higher doses of ASP3082 by itself, or together with cetuximab. Any medical problems will be recorded at each dose. This is done to find suitable doses of ASP3082, by itself or together with cetuximab, to use in Part 2 of the study. The first group will receive the lowest dose of ASP3082. A medical expert panel will check the results from this group and decide if the next group can receive a higher dose of ASP3082. The panel will do this for each group until all groups have received ASP3082 (by itself or together with cetuximab) or until suitable doses have been selected for Part 2.

In Part 2, ASP3082 will be given in by itself, or in combination with the other study treatments.

Study treatments will be given through a vein. This is called an infusion. Each treatment cycle is 21 or 28 days long. They will continue treatment until: they have medical problems from the treatment they can't tolerate; their cancer gets worse; they start other cancer treatment; or they ask to stop treatment.

This is an umbrella study evaluating the efficacy and safety of multiple treatment combinations in participants with metastatic or inoperable locally advanced breast cancer.

The study will be performed in two stages. During Stage 1, four cohorts will be enrolled in parallel in this study:

Cohort 1 will consist of Programmed death-ligand 1 (PD-L1)-positive participants who have received no prior systemic therapy for metastatic or inoperable locally advanced triple-negative breast cancer (TNBC) (first-line \[1L\] PD-L1+ cohort).

Cohort 2 will consist of participants who had disease progression during or following 1L treatment with chemotherapy for metastatic or inoperable locally-advanced TNBC and have not received cancer immunotherapy (CIT) (second-line \[2L\] CIT-naive cohort).

Cohort 3 will consist of participants with locally-advanced or metastatic HR+, HER2-negative disease with PIK3CA mutation who may or may not have had disease progression during or following previous lines of treatment for metastatic disease (HR+cohort).

Cohort 4 will consist of participants with locally-advanced or metastatic HER2+ /HER2-low disease with PIK3CA mutation who had disease progression on standard-of-care therapies (HER2+ /HER2-low cohort).

In each cohort, eligible participants will initially be assigned to one of several treatment arms (Stage 1). In addition, participants in the 2L CIT-nave cohort who experience disease progression, loss of clinical benefit, or unacceptable toxicity during Stage 1 may be eligible to continue treatment with a different treatment combination (Stage 2), provided Stage 2 is open for enrollment.

The main purpose of this study is to assess safety \& tolerability and antitumor activity of LY3962673 as monotherapy and in combination with other chemotherapy agents in participants with KRAS G12D-mutant advanced solid tumor types. The study is expected to last approximately 5 years.