Composition?

    typedef struct { /* ... */ } context;
    typedef struct {
      context ctx;
      /* ... */
    } foo_context;
    typedef struct {
      context ctx;
      /* ... */
    } bar_context;

    void some_general_method(context* ctx, int a, int b);
    void some_foo_specific_method(foo_context* foo_ctx, int c, int d);

    foo_context* foo_ctx;
    some_foo_specific_method(foo_ctx, 0, 0);
    some_general_method(&foo_ctx->ctx, 1, 1);

For checked downcasts, you could include an enum type tag inside `context` and have something like `foo_context* as_foo_context(context* ctx)` for downcasts, which, if `context` is at the beginning of `foo_context`, could just check the tag and cast the `ctx` pointer to `foo_context*` (or do a little pointer arithmetic if `context` is somewhere else in the containing struct). Return `NULL` (or assert) if the tag doesn't match.