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That's going to be a problematic situation for the agents, and I'm actually not sure I'd recommend using the Genesys Cloud for Salesforce integration in that scenario. Where you're going to run into trouble is with call logging in particular; the softphone is going to attempt to save the call log into which ever Salesforce instance the agent answers the call in, and if they switch tabs you'll start to see errors attempting to save the call log because the object ID doesn't exist in that 2nd/3rd Salesforce instance. Screen pops will also be somewhat questionable, as the screen pops will be using search criteria that is very likely specific to a single instance of Salesforce; if that search criteria is used in a different Salesforce instance, you'll either get no screen pop or a screen pop to the incorrect object.
The best case scenario is to consolidate to a single Salesforce instance (which I've seen Salesforce recommend to other customers that have found themselves in the same position). This will greatly simplify the Agent's experience, and prevent the sorts of issues that come from operating out of multiple Salesforce instance at the same time (like call log saving errors).
In the interim, I'd recommend looking at the Genesys Cloud for Chrome browser extension, which will allow for embedded call controls, webRTC, etc. as a part of the browser, and can screen pop to complete URLs (which should inherently point to the correct Salesforce instance, at least in the event that "myDomain" has been enabled, as this will contain a unique domain name as the prefix to the URL).
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