I need more VRAM because otherwise I won't be able to play a game.
The point, however, is that I have a laptop with an integrated graphics card, so it is not possible to switch. Is there still a way to increase my VRAM?
With chipset graphics this can sometimes be set in the BIOS.
If there's a real graphic in it, then of course not.
If there's a real graphics card installed then that is not possible. If this is a graphics unit in the processor or from the chipset, you can possibly set in the BIOS that more RAM is available for the graphics unit.
But then this is not a "real" VRAM and will probably not fulfill the purpose you are aiming for.