Just thought of this nuzlocke and I thought I might share it!
I'll dub it the Semi-solocke.
-=RULES=-
1) Fainted pokemon are dead, as per usual.
2) You must catch every new pokemon encountered, no exceptions. (New being if you have not caught it yet)
3) You can only use one pokemon at a time, all captured pokemon must be stored in a pokemon box.
4) Once a pokemon dies, it must be stored or released and the next pokemon you captured must be put into your team
4a) If your next pokemon is seriously underleveled you can use your dead pokemon to help it level up, it is now a ghost.
4b) Once your pokemon is at a high enough level, the ghost must be released
5) You can have HM slaves, but they cannot be used in battle.
6) You lose if all of your pokemon stored in the box are dead (this probably won't happen though )
That's pretty much it, have fun!