This is a common problem with a terminal that we manufacture. It has no MAC address burned into the hardware and spoofs one on first boot. One of the problems we have is that the address is (supposedly random) generated by the system clock but if the terminal hasn't been tested it will boot with all ones (as in 11/11/11/ time 11.11) and create the same MAC address.
Two points here 1) an OUI is an International physical address so the reply above that all MAC addresses are internationally unique is not correct.
And 2) in my experience I have found issues that vary from an ARP storm on a small network switch with auto negotiation on a class C only network to no more than not being able to resolve the address (the ARP) despite the terminals having different IP addresses.
Also a hub would not work. Although a hub has no requirement for the physical address you still have an argument that cannot be resolved. ie: you cannot, ever, under any circumstances, have the same physical address on the same network or domain. The whole point of the MAC address is to know where to send the signal.
Also this isn't a case of two objects in the same space and time because that isn't how medium access works. The problem is no ARP return so although Joe Qwerty is largely correct the proposition that a single host can have mutliple IP addresses is ambiguous. A host can have multiple NIC's and that would mean multiple IP's and multiple MAC's. Maybe he means multiple IP's on a single NIC but actually although that is possible you can only use one IP address at a time but yes they would both have the same MAC but they wouldn't both be online at the same time. Also if the host had multiple NIC's they would be multiple hosts.
Back to your question - if one host is cloning the others MAC can you not change the MAC using a DoS prompt? What is the hardware? Many years ago with cable broadband you had to clone your NIC to the modem and that didnt matter because the MAC is an external physical address and not used in the local host network so there is no conflict to begin with
bit off topic I know but wanted to address the errors in the above answers (apart from Joe qwerty that is)