  Motivated by the possible existence of other universes, with possible
variations in the laws of physics, this paper explores the parameter space of
fundamental constants that allows for the existence of stars. To make this
problem tractable, we develop a semi-analytical stellar structure model that
allows for physical understanding of these stars with unconventional
parameters, as well as a means to survey the relevant parameter space. In this
work, the most important quantities that determine stellar properties -- and
are allowed to vary -- are the gravitational constant $G$, the fine structure
constant $\alpha$, and a composite parameter $C$ that determines nuclear
reaction rates. Working within this model, we delineate the portion of
parameter space that allows for the existence of stars. Our main finding is
that a sizable fraction of the parameter space (roughly one fourth) provides
the values necessary for stellar objects to operate through sustained nuclear
fusion. As a result, the set of parameters necessary to support stars are not
particularly rare. In addition, we briefly consider the possibility that
unconventional stars (e.g., black holes, dark matter stars) play the role
filled by stars in our universe and constrain the allowed parameter space.
