  We explore equilibrium solutions of spherically symmetric boson stars in the
Palatini formulation of $f(\mathcal{R})$ gravity. We account for the
modifications introduced in the gravitational sector by using a recently
established correspondence between modified gravity with scalar matter and
general relativity with modified scalar matter. We focus on the quadratic
theory $f(\mathcal{R})=R+\xi R^2$ and compare its solutions with those found in
general relativity, exploring both positive and negative values of the coupling
parameter $\xi$. As matter source, a complex, massive scalar field with and
without self-interaction terms is considered. Our results show that the
existence curves of boson stars in Palatini $f(\mathcal{R})$ gravity are fairly
similar to those found in general relativity. Major differences are observed
for negative values of the coupling parameter which results in a repulsive
gravitational component for high enough scalar field density distributions.
Adding self-interactions makes the degeneracy between $f(\mathcal{R})$ and
general relativity even more pronounced, leaving very little room for
observational discrimination between the two theories.
