How should I widen a picture frame?
A block plane will work up to a point. Use it parallel with the grain, and in the direction that the wood grain is rising (since no grain is perfectly parallel) to avoid tear-out. They make some wood planes without sides, which can be useful for corners, but may risk tear out for your purposes.



Instead, the design with a blade near the very front may be the best for this task:



With each of these, you'll eventually need to carefully chisel out the corner.