You're on the 3rd gen processor from Intel.Right now, taxing your system with current gen games will demand more from the system. If you add streaming to the list of tasks, you will have unfavorable results(when streaming and gaming at the same time).
According to this PDF, you're limited to 3rd Gen processors as the top most series. I would suggest getting an i7-3770K but you're going to have to do a BIOS update but that wont be a significant upgrade with what you plan on doing.
You should also list the sort of games you play at the moment and plan to play in the future. Also list the tasks you do(please don't include etc in that sentence) so as to understand what you actually need.
Make and model of the PSU?