There are opportunities to move up to tier 2 support which is just the next level higher. There some possible opportunities to eventually try and become a team manager, but every manager I know, it has taken a few years to get there. I'm not even sure how great a position that would be.
You could also move to other queues that are more specialized, like pro apps, or wireless multi media etc. I think these may just be lateral with no benefit, or not much of one in pay. If you want to move to Austin, or Cupertino, I'm sure there are many more options to move up, but as for being at home, you are limited and at the complete mercy of the customer.
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Our TIA was as much as 11-12 min during Christmas. We were way overstaffed.