A Study of XMT-1660 in Participants With Solid Tumors

Inclusion Criteria: * Recurrent or advanced solid tumor and has disease * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 * Participants in DES must have at least one non-target lesion as defined by RECIST version 1.1. Participants in Backfill Cohorts and EXP must have at least one measurable disease (target) lesion as defined by RECIST version 1.1. * Tumor tissue, either archival or from a fresh tumor biopsy, available for testing or be willing to undergo a minimally invasive tumor biopsy to obtain tumor tissue for local testing, if not medically contraindicated, prior to Cycle 1 Day 1 * Brain magnetic resonance imaging (MRI) during the Screening period unless obtained within 30 days prior to Screening (based on standard clinical care), if they meet either of the following criteria: 1. All participants with TNBC 2. Participants with a history of brain metastases or with neurologic symptoms or signs suspicious for brain metastases. Exclusion Criteria: * Prior treatment with an Antibody Drug Conjugate (ADC) containing an auristatin payload. Prior treatment with another ADC containing other payloads is allowed. * Major surgery within 28 days of starting study treatment, systemic anticancer therapy within the time period of 28 days or 5 half-lives of the prior therapy before starting study treatment (14 days or 5 half-lives for small molecule targeted therapy), whichever is less, or palliative radiation therapy to the chest within 3 months of starting study treatment or to other anatomic sites within 14 days of starting study treatment. * Diagnosis of additional malignancy that required active treatment (including surgery, systemic therapy, and radiation) within 2 years prior to screening, except for adequately treated basal cell or squamous cell skin cancer, or carcinoma in situ of the breast or of the cervix. * Untreated CNS metastases (including new and progressive brain metastases), history of leptomeningeal metastasis or carcinomatous meningitis. * Prior B7-H4 targeted treatment. * History of cirrhosis, hepatic fibrosis, esophageal or gastric varices, or other clinically significant liver diseases. * Current severe, uncontrolled systemic disease (e.g. clinically significant cardiovascular, pulmonary, or metabolic disease) or intercurrent illness that could increase the risk of serious adverse events (SAEs) or interfere with per-protocol evaluations, in the judgment of either the Sponsor or the Investigator. * Clinically significant cardiovascular disease