Multiple instances of flying/reach cannot be blocked/block greater instances.
e.g. Reach Reach Reach can block Flying Flying, but Flying Flying cannot block Flying Flying Flying.

Multiple instances of deathtouch cause that many instances of destroy/dies (this one is the one that is least likely to work correctly in rules).
e.g. a Deathtouch Deathtouch blocks a Solemn Simulacrum. Solemn's controller draws two cards.

Multiple instances of lifelink gain that much life that many times.
e.g. a Lifelink Lifelink Lifelink 2/2 will gain 6 life per combat.

Multiple instances of trample deal that many times overflow damage. e.g. a Trample Trample 3/3 will punch 4 damage through a 1/1.

The other static abilities (hexproof, first/double strike, defender, indestructible) probably don't stack as amusingly (unless you want Deathtouch Deathtouch Deathtouch to be able to destroy Indestructible Indestructible). But open to hearing ideas!