We present an extension of our quasi-linear numerical method for the time-dependent spherical harmonics (Pn) equations. The extension involves adding time integration that is higher order than backward Euler, yet avoids artificial oscillations in the solution. This new approach mimics that of our previously presented quasi-linear spatial scheme in that we use a first-order step to determine in which parts of the problem we can use a high-order method. The first-order scheme we use for time integration is backward Euler, and the high-order method we implement is Crank-Nicolson. Results are presented that demonstrate the effectiveness and necessity of this approach.