Having a machine report to multiple Core Servers isn't supported. The certificates exist to help the client validate that the correct Core Server is talking to it. Usually you will have multiple certificates due to upgrades, migrations, or potentially consolidation. You can put the appropriate certificates on the Core and/or clients to help them communicate, however the client will still only report to and work with a single Core Server.
You may be interested in the information here: How to run an Agentless Inventory scan on multiple computers from the Core Server with LDDiscover.exe
Also, make sure you don't have 2 Core Servers pointing at the same database, as that will cause a number of problems.