Title requirements double closing LLC

I am about to do a double closing, AB then BC. Can the B buyer(s) use an LLC for the first transaction then add the C buyer to the LLC? Then the B buyer(s) would sell their shares of LLC to C and walk away.
Would this eliminate the need for for the BC closing? My theory is that the C buyer is now in control of LLC, and this eliminates any seasoning that may be required. Can you guys show me the holes in this theory?

Thats not a double closing… Its a single closing and a business transaction. You could do the similar thing with a corporation but why not use a trust if that is what you anticipate doing or become a line item on the HUD1 and make it a A to C transaction…

Good Luck