No. The Nintendo DSi has only one Game Card slot. It cannot read two or more cartridges simultaneously. "Multi-Card Play" (local wireless multiplayer where each player inserts their own copy of the game) requires each player to have their own DSi/DS/3DS system with the game inserted.
If you want multiple players, each needs a DSi/3DS and their own game card (or the host uses Single-Card Download Play if the title supports it).