  It is well known that Feynman integrals in dimensional regularization often
evaluate to functions of hypergeometric type. Inspired by a recent proposal for
a coaction on one-loop Feynman integrals in dimensional regularization, we use
intersection numbers and twisted homology theory to define a coaction on
certain hypergeometric functions. The functions we consider admit an integral
representation where both the integrand and the contour of integration are
associated with positive geometries. As in dimensionally-regularized Feynman
integrals, endpoint singularities are regularized by means of exponents
controlled by a small parameter $\epsilon$. We show that the coaction defined
on this class of integral is consistent, upon expansion in $\epsilon$, with the
well-known coaction on multiple polylogarithms. We illustrate the validity of
our construction by explicitly determining the coaction on various types of
hypergeometric ${}_{p+1}F_p$ and Appell functions.
