Let $M$ be a $\pi_*(MU)$-module. The Landweber exact functor theorem gives conditions for the functor that sends a space $X$ to $ MU(X) \otimes_{\pi_*(MU)} M$ to define a homology theory on spaces, which thus comes from a spectrum.

It'd be nice, though, if one could construct the spectrum directly, instead of going through the homology theory. For instance, it would be nice if one could construct an actual $MU$-module (possibly under further hypotheses) or an $MU$-algebra when $M$ is an algebra. Is there another version of the exact functor theorem that lets one do this?