You cannot have the same IP network on different layer 3 interfaces of the same gateway device (router or layer 3 switch, firewall, etc.) without the use of a feature like VRF to logically segment the networks from each other into separate forwarding tables.
You can have different IP networks on different layer 3 interfaces of the same gateway device and use NAT to make them appear to act as the same IP network to a degree.
If the networks in question are connected via different gateway devices then you can have the same IP network on the two networks but for them to communicate directly you need a combination of features to make each network appear as a connected network or as a different network (VXLAN, VPN, Tunneling of some kind, etc.).
If you meant hosts in the same single network separated by a basic layer 3 gateway, then no, once you have a layer 3 gateway in between devices, it is no longer a contiguous network (unless you have other special features again to make it work as a single network).
If you simply mean 'does multicast work over routers?' then yes, multicast routing is a feature available on many business class routers.