A Riemannian manifold $ M' $ is Riemannian homogeneous if $ Iso(M') $ acts transitively.
A Riemannian manifold $ M $ is locally Riemannian homogeneous if there exists a Riemannian homogeneous manifold $ M' $ such that $$ M \cong \Gamma\backslash M' $$ where $ \Gamma $ is a discrete subgroup of $ Iso(M') $.
Every orientable surface admits a locally Riemannian homogeneous structure (moreover locally symmetric moreover constant curvature).
For the non orientable case I know that the projective plane is Riemannian homogeneous, while connected sums of multiple projective planes are never Riemannian homogeneous. But what about locally Riemannian homogeneous? For example
Can the connected sum of 3 projective planes be given a locally Riemannian homogeneous structure?