Changing an SLA property after reassigning an incident ticket from one group (different SLAs) to another group

Changing an SLA property after reassigning an incident ticket from one group (different SLAs) to another group

I'm having an issue with the following scenario - >Workflow is an email request gets submitted to group#1 who has defined SLAs.  They cant resolve the issue and assign the ticket to Group #2 who had different SLAs than group #1.   It doesnt appear you can automate (not sure) changing the SLA to the receiving groups SLA or even manually changing it.  

Is anyone aware of how to address this?

Thanks 
Ed M 

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