  Using purely variational methods, we prove local and global higher
integrability results for upper gradients of quasiminimizers of a
$(p,q)$-Dirichlet integral with fixed boundary data, assuming it belongs to a
slightly better Newtonian space. We also obtain a stability property with
respect to the varying exponents $p$ and $q$. The setting is a doubling metric
measure space supporting a Poincar\'e inequality.
