Here is a diagram of the situation.

Collision planes are the red dashed lines, contact normals in green.
The object is initially not touching the walls. After moving one time step to the right, the object overlaps the two spikes as well as the right wall. There is no way out of this trap, because the contacts cannot be simultaneously solved.
My update logic is roughly as follows:
- Broad+Narrowphase: Find all contacts.
- Find closest valid displacement to the object's desired displacement with PGS. If PGS cannot resolve collisions within some threshold, zero the displacement.
- Move object by the corrected displacement.