Background: Downstaging— reduction in late-stage incidence—has been proposed as an endpoint in randomized trials of multi-cancer early detection (MCED) tests. How downstaging depends on test performance and follow-up has been studied for some cancers but is understudied for cancers without existing screening and for MCED tests that include these cancer types. Methods: We develop a model for cancer natural history that can be fit to registry incidence patterns under minimal inputs and can be estimated for solid cancers without existing screening. Fitted models are combined to project downstaging in MCED trials given sensitivity for early- and late-stage cancers. We fit models for 12 cancers using incidence data from the Surveillance, Epidemiology, and End Results program and project downstaging in a simulated trial under variable preclinical latencies and test sensitivities. Results: A proof-of-principle lung cancer model approximated downstaging in the National Lung Screening Trial. Given published stage-specific sensitivities for 12 cancers, we projected downstaging ranging 21%-43% across plausible preclinical latencies in a hypothetical 3-screen MCED trial. Late-stage incidence reductions manifest soon after screening begins. Downstaging increases with longer early-stage latency or higher early-stage test sensitivity. Conclusion: Even short-term MCED trials could produce substantial downstaging given adequate early-stage test sensitivity. Impact: Modeling the natural histories of cancers without existing screening facilitates analysis of novel MCED products and trial designs. The framework informs expectations of MCED impact on disease stage at diagnosis and could serve as a building block for designing trials with late-stage incidence as the primary endpoint.