Some silly ideas:
Mine every single rock in runescape (I have actually done this!)
Chop every tree, craft every craftable object, kill every monster, fletch every fletchable object etc.
Collect every rare, then destroy them all.
Buy the maximum possible number of runecoins. Could be anything from 2k runecoins to 2b runecoins.
Buy out the Grand Exchange by creating hundreds and hundreds and between them, offering max cash for every item.
Interact with every npc/item in every possible way.
I personally count as a comleteable anything that is permanent about your character, can be viewed by the player, and can be maxed out. So the number of castle wars games played counts, as (i) they are permanent (ii) can be viewed by player (iii) can be maxed out.
But the number of trouble brewing games played isn't 'completable', even if the jagex servers store that information, as the player cannot view it.
Using this as a guide, other examples not included in the trimmed comp requirements would be:
Reach 255 in endurance and climber mode in Dominion Tower.
Collect all optional quest rewards, like all 5 lamps for running supplies to Burthorpe archers, the one-time craft and prayer exp for making an illuminated holy book etc.
Collect a piece of all hybrid armour (the armour itself is not permanent, but the increased probability of obtaining a piece is).
Unlock all rewards from the crucible.
Unlock the highest tier in Windstalker and Duelist hats.
That's all I can think of for now.