Basement Renovation - Column Move?
Three feet doesn't sound like much, but for a high-stress beam it is. You'll probably need to convert from solid wood to LVL or steel at a prescribed size.  As you say, most of the weight of the home is on the block foundation. That still leaves a few tons on the beam, and you don't guess with that kind of load.

The larger problem, though, is that you may not have a footing where you'd like the post to go. It's typical to see a 36" square footing poured under the slab at point locations such as this, and you'd need to cut open the floor to add a new footing (10-12" thick on undisturbed soil). Not doing so would probably result in settling and cracking of the slab, and therefore sagging of your house in undesirable ways. 

Get a professional to take a look with you. This is no question for a bunch of yahoos on the internet.