One of the informal, but well-known, rules of block design in R&D has to do with the types of counters that are put on creatures. In order to avoid game state confusion, in an expert-level expansion, there shouldn't be both +1/+1 counters and -1/-1 counters produced by cards in the same block. This was, of course, one of the ways to show how Shadowmoor block was the dark mirror of Lorwyn block, as well as the everpresent corruption of the Phyrexians in Scars of Mirrodin block, so the humble -1/-1 counter has proven itself to be a useful and flavorful design tool since its reintroduction into widespread use (Shambling Swarm and Quagmire Lamprey were just oddities).
However, despite their welcome return after years of never being used in new cards, -1/-1 counters haven't shown up again in a block since Scars of Mirrodin. They have lots of fans, and are due for another shot - +1/+1 counters lend themselves to more designs than do their evil opposite, so they're way more prevalent, but by no means the new norm - so here's how they could be used in the future. Wither, infect, and persist have all been popular keywords involving -1/-1 counters, but a new block also needs new mechanics.
Reverse graft. Yes, as in entering the battlefield with a bunch of -1/-1 counters - but then shunting one off whenever a creature entered the battlefield under an opponent's control. This is repeatable removal that also grows your creature, so this would have to be pretty conservatively costed, but man would that be satisfying. Also possible is a modular variant, i.e. Grief Tyrant keyworded. I've seen this called "contagion" in custom cards, and even literally "graft -N."
Weakening as a discount. Every block needs its kicker variant keyword, so something like the unholy opposite of monstrosity - paying a smaller amount to have your creature spell enter the battlefield with a certain number of -1/-1 counters - would be appropriate for some worlds. I've seen brutal low-fantasy set concepts that called this one disfigure, which is a gruesomely flavorful name, and if people like evoke then they'd like this mechanic.
Paying in blood. Imagine a kind of convoke variant here where you can make your creatures take -1/-1 counters in exchange for a mana discount. A mechanic that were a straight-up "Putting a -1/-1 counter on a creature you control pays for one mana" would get degenerate, so it could be restricted to only one counter per creature (possibly too similar to convoke), or only using one creature but up to as many counters as it has toughness points, or perhaps only until it has 1 toughness so you can't kill the victim, just drain off a lot of blood, so to speak.