  In this paper we study the cosmological aspects of metric-affine $f(R)$
gravity with hyperfluid. The equations of motion of the theory are obtained by
varying the action with respect to the metric and the independent connection.
Subsequently, considering a Friedmann-Lema\^itre-Robertson-Walker background,
we derive the modified Friedmann equations in the presence of a perfect
cosmological hyperfluid. Especially, we focus on the particular case in which
$f(R)=R+\beta R^2$, considering purely shear hypermomentum and finding exact
solutions in the weak coupling limit.
