An alternative is to have different movement functions for your character (e.g. walking, freefall, in water, climbing a ladder, wallrun, etc.) that are called each frame by a master function that checks whether the character is on the ground, hugging a wall, and so on, where the standard gravity applies only in some of these functions. The old Quake 3 Arena used to work this way; its collision detection is very robust - no objects clip through walls, no matter how small and fast, and, if you're working with a simpler engine or want to code the physics/collision detection from scratch it may be of inspiration.

This is an idea I've been having for a while:

A team-based multiplayer game. I've imagined it as fantasy themed.

During the first phase of the game, each team (among two, or perhaps more) is assigned a section of a randomly generated map. The players are tasked with building a fortification and buying equipment/upgrades with a set amount of resources and in a limited time (say, a few minutes). During this phase, the interface is similar to that of a RTS.

Once this is done, each player takes control of a character as they set upon their opponent's base. A team can win by either capturing/destroying a critical part of the enemy's base or depleting their spawn points by killing the enemy players enough times. During this phase, the game plays more like a FPS/TPS/Hack 'n' slash or the like.

Probably very hard to attract players with this, but hey, this is the hopeless idea thread after all...