There is a way to run an application as another user, but I don't believe it works for addins or other DLLs. DLLs run attached to other processes, and I don't think there is a way to do that while running as a user different from the owning process.
For EXEs, there are ways to run as another user.
In case anyone is interested, I figured out how to do this. Basically, you create another vault instance (vaultRename) and log into that vault instance with the desired user ("Rename"). Then use the new vault instance with the rest of your code.
Dimvault As IEdmVault11
DimvaultRename As IEdmVault11
vault = poCmd.mpoVault
vaultRename = New EdmVault5