Turok: Rage Wars: 1999
Developer: Bit Managers S.L.
Instead of the usual Turok single player missions, you must control your character and complete certain missions (from getting the most frags in a time limit, finding an item, or lasting the distance). Before a match you also get to choose which weapons to use, and you can unlock heaps of more weapons and character skins as you complete the objectives.
Multiplayer is the main aim of this game, and there are plenty of 4 player game modes to choose from (frag and tag, capture the flag, Bloodlust, etc.) as well as a 2 player co-op Trial mode (much like the single player missions) time trials and frag fests.