There's a sizeable courtyard behind one of the buildings (currently an atrium) from which an elevator core could possibly rise and the former alleys that are now mall passageways from which supporting columns could also rise.
So in theory, they could keep the buildings intact, with maybe some additional columns in places - like The Exchange
- or as mentioned, just preserve the façade.
Here's the aerial from Bing:
https://www.bing.com/search?q=sinclair+centre&src=IE-SearchBox&FORM=IENTTR&conversationid=
Threaded Mode