With the Push/Pull tool active … Look to the Status Bar at the bottom of the GUI
There, notice you can use a modifier key to create a new starting face.
Press Ctrl (Microsoft Windows) or Option (Mac OS X) and the Offset Limit is negated.
When that P/P operation doesn’t create the edges of intersection you need:
• Select the geometry
• Right Context Click on the selection > Intersect Faces > With Selection
• Then erase what you don’t need.
