  A meromorphic quadratic differential on a compact Riemann surface defines a
complex projective structure away from the poles via the Schwarzian equation.
In this article we first prove the analogue of Thurston's Grafting Theorem for
the space of such structures with signings at regular singularities. This
extends previous work of Gupta-Mj which only considered irregular
singularities. We also define a framed monodromy map from the signed space
extending work of Allegretti-Bridgeland, and we characterize the
PSL(2,C)-representations that arise as holonomy, generalizing results of
Gupta-Mj and Faraco-Gupta. As an application of our Grafting Theorem, we also
show that the monodromy map to the moduli space of framed representations (as
introduced by Fock-Goncharov) is a local biholomorphism, proving a conjectured
analogue of a result of Hejhal.
