Yes, you can change the MAC address of most newer NICs, but it's generally a bad idea in a network situation because duplicate MAC addresses can occur. These are extremely difficult to diagnose in large networks.
No, you can't have more than one MAC address per NIC. Multiple IP addresses YES, multiple MAC addresses NO. This is because the MAC address is a hardware address representing a single piece of hardware (NIC). An IP address is a logical network address - one NIC or network interface can belong to more than one network & therefore have more than one IP address.
Having two IP addresses with the same MAC should not cause problems - is there a specific reason why you would be concerned?