If you do the Back to Back using different airlines then this should be OK
Example
Fly CLE-LGA Sat AM UA
Fly LGA-CLE Sat PM DL
Fly CLE-LGA Mon AM DL to get to NYC to get my UA return
FLY LGA-CLE Mon PM UA
This is Back to Back ticketing but not legal if it was UA. Since it is different airlines
UA and AA won't be aware of this, only God knows. The reason I would do this is I get 2 full days in NYC, but no hotel bills. I did this one time many years ago on CO when they had the EWR weekend special of $79:00 RT. I thought when I to book the EWR-CLE RT to avoild the Sat night stay the reservation system would not take this buit it did.