there are basically two parts involved in SNMP monitoring:
1.) polling values from SNMP devices (like CPU, bandwidth, etc.)
2.) receiving traps (events when something goes wrong)
Polling the values will work from multiple SNMP management systems but for SNMP traps, it depends on the device if it is possible to setup more than one trap receiver. There are also trap forwarders allowing you to receive a single trap and distribute them to multiple systems. In fact some SNMP managers can receive traps and at the same time forward it to another system.