How many profiles do we need?

Summary:

I'm trying to figure out, in furtherance of economy, how few profiles we need for our organization.

Content (required):

Greetings hivemind. In our organization, we have essentially three areas/topics on which staff our trained, and each of those topics has its own incident queue. It takes roughly a year for people to be fully trained to handle incidents on all three topics. Generally, when they are hired they are trained on only one, then the other two in turn.

I would like, if possible, to have just two profiles:

1) one for 'fully trained' (all 3 topics) staff which would see incidents assigned to them automatically (no 'fill inbox'), as long as they are logged in.