Is there one interface for searching all or multiple libraries?

In a meeting recently, we did an online search to connect to an EndNote library at Princeton & then Columbia. The connection to Princeton was taking a long time and as we were waiting, someone asked if there was a way to do the online search without specifying particular libraries.

I wasn’t sure how to do that. In the past, I created connections to individual libraries and searched. I can see the utility of searching all libraries, but I’m not sure if it’s feasible…does such a capability exist already? (If I understand online searching/connection files correctly, then I sort of think that this global-connection/search feature doesn’t/can’t exist?)

EndNote tech support confirmed that you can’t search multiple ENLs simultaneously; searches of ENLs have to be done individually.