Just using ReVamp, it's theoretically possible to have more than 3 of an enemy on the screen. Don't get your hopes up just yet; it's quite difficult to pull off and the circumstances require the cooperation of the player. In other words, the chances are slim-to-none.

This is due to a shortcut in the coding. Some enemies like mummies search for pre-existing versions in the range of 1 to 8, but when they spawn they look for free slots in the range of 1 to 12. That means as long as slots 1 to 8 are full and don't contain more than 2 of the current type, the next enemy will spawn outside the range of the multiplicity check.

It's still not as easy as it sounds. You can only have four enemy spawners per screen. Not all enemies will spawn in the same range and most enemies won't stay on the screen long enough to harass Trevor. This could in theory, perhaps, be achieved with 3 Ghost spawners, 3 Fleaman spawners, a Slime spawner, and then a Mummy spawner. The player would have to flee from the ghosts, Fleamen, and Slime so all 7 are on screen at once, the encounter the mummy. On the first iteration, two mummies will spawn. In theory, on the second iteration, two more will spawn in slots 9 and 10, allowing for two more to spawn in slots 11 and 12 on the next iteration assuming there are no bandages being tossed, since bandages will occupy slots 9 to 12.