Stillman's conjecture states that there is a bound on the projective dimension of homogeneous ideals in a standard graded polynomial ring which depends only on the number and degrees of the generators of the ideal and importantly not on the number of variables in the polynomial ring. This was proven by Ananyan and Hochster in 2016, and reproven by Erman, Sam, and Snowden and Draisma, Laso\'n, and Leykin in 2019 using novel techniques. Inspired by recent interest in toric geometry, we investigate the existence of Stillman bounds when the polynomial ring is multigraded by an abelian group. Using a new multigraded version of Los’s theorem from model theory, we utilize ultraproducts (as did Erman-Sam-Snowden) to give an exact characterization of the gradings which admit Stillman bounds. This is joint work with John Cobb (Auburn University) and John Spoerl (UW Madison).