  We continue our study, initiated in our earlier paper, of Riemann surfaces
with constant curvature and isolated conic singularities. Using the machinery
developed in that earlier paper of extended configuration families of simple
divisors, we study the existence and deformation theory for spherical conic
metrics with some or all of the cone angles greater than $2\pi$. Deformations
are obstructed precisely when the number $2$ lies in the spectrum of the
Friedrichs extension of the Laplacian. Our main result is that, in this case,
it is possible to find a smooth local moduli space of solutions by allowing the
cone points to split. This analytic fact reflects geometric constructions in
papers by Mondello and Panov.
