Be very careful with this. Yes, you can buy a 2nd co-op apartment in the same building where you live. Beware you will face several issues:
1. Ask the members of the co-op Board if this is permitted. I don't know the House Rules for your co-op and you need to verify if this is permitted under the By-Laws. Also verify this with the co-op building attorney. Property Management does not need to get involved. Only the attorney.
2. Will the 2nd apartment (the one you plan to live in) be paid for in cash or will you need financing? If paying in cash - no problem. However, if you need a mortgage loan, beware that lenders will not have you own 2 apartments as primary residences. They may consider the 2nd apartment as an investment and charge you a higher interest rate + a higher down payment because it's not a primary residence.