Here's some:
Headshots only count during sniper rampages, body shots won't.
A skull icon to show where the rampage is, like the 3D rampages.
Remove the player abilities during specific rampages, Michael's ability during sniper rampages, Franklin's ability during drive-by rampages, and Trevor's ability during melee rampages.
No rampages where you need to kill random npc's, only gangs or vehicles.
Enemies during melee rampages should be one hit, and be armed with pistols, knives, and bats.
I might have some more details later on.
More possible rampage objectives:
Blow up 20 Ballas in 2 minutes (RC Bandito) reference to "Triad Takedown" in GTA: Liberty City Stories!
Destroy 30 Vagos lowriders in 3 minutes (Compact Grenade Launcher)
Hard-scope 15 Marabunte Grande members in 2 minutes (Marksman Rifle)
Whack 80 Armenian mobsters in 4 minutes (Gusenberg Sweeper)
Mow down 100 Rednecks in 5 minutes (Combat MG)
Run over 30 Street Punks in 2 minutes (Vehicle)
Snipe 15 Cartel members (Cayo Perico guards) in 2 minutes (Sniper Rifle) This one must be one on of those guard towers in CP.
Terminate 30 Lost MC members in 3 minutes (Sawn-Off Shotgun) Must be on a bike during this.
Annihilate 50 Families Gang members in 2 minutes (RPG)
Slice and Dice 20 Marabunte Grande members in 3 minutes (Machete)
Explode 30 Triads in 2 minutes (Sticky Bombs)
Exterminate 40 Professionals in 3 minutes (Advanced Rifle)
Eliminate 25 Rednecks in 2 minutes (Double-Action Revolver)
Some random ones I thought of:
Destroy 20 Oppressors in 3 minutes (Rail Gun)
Launch 30 tryhards in 4 minutes (Up-N-Atomizer) Enemies must be one shot during this.
Burn 15 Altruist members in 2 minutes (Flare Gun)
Neat that someone actually hears one of my ideas, thanks for noticing!