When buying a large multi-family building, other than the home inspector, what type of specialist can further evaluate structural integrity, foundation, sagging, etc? Would it be Structural Engineer?  

Eric,  there are structural inspectors who can help you. I would ask your local contractor for a referral for this. Some Physical (General) Inspectors are contractors and can give you limited intuition into the structural condition based on their experience, however, YES, you would need a Structural Engineer.  

A licensed P.E. (Structural)