Cigna and Aetna

At my fulltime employer I have Cigna.  It will pay for bariatric surgery, and I have to pay 20% after the $350 deductable, no more than $2000.  My lab fees are the same.(upper GI, bloodwork, etc) I have the opportunity to pick up a limited coverage at my part time job, with Aetna.  My question is, while I know Aetna will not cover the surgery -- can I use them as a secondary insurance to pick up some of what Cigna does not?