You can play Elise however you want to, breh.
**Carry **=
Note: You have to have some extremely safe positioning and skills, and/or a skilled enough team that can properly peel enemies off of you.
AP-Based-Damage Off-Tank =
Note: pretty standard ap-tank build. Build resistances as needed. Feel free to explore other items, and definitely don't limit yourself to only the sequence of items I've suggested within this post.
Item-Based-Damage Off-Tank =
Note: You rely on being within melee range more often than not, and adc needs to attack you in order for you to benefit from Thornmail. Really tanky against AD, but you can still easily be 100-0'd if you're not playing safe enough. Elise's kit offers great ap scaling, and thus this particular subset of items isn't optimal on her. It still works, but AP items are superior in terms of damage.
Full Tank =
Note: Elise doesn't scale with armor, hp, or mr. So you'll be extremely weak in terms of damage, especially if the enemy team builds even a morsel of defense against you. Build these if you have too many glass-cannon carries in solo queue, and/or want to trollololol around.
Tank Boots =

Here're some cheese builds:
Tank Shredder/Carry Crippler

and
Surprise Muthafuka! [snowballing required]

You're welcome.