Beam jacking is as much art as science. It is a close cousin to house moving. The rate of increase must be gradual to prevent floor covering damage, wall damage and water and gas pipe damage.
The absolute amount you wish to lift will determine what is safe.
It may be that sistering new joists alongside the "water softened" ones is what you really need. A temporary jacking beam can be used to place the new joists and removed after they are lagged in place. Hopefully you can span from beam to side wall.
Beam construction design is based on material used (steel, glulam, fir), span distance (beam support to beam support) and load (the weight transferred from the joists above. As commented by DA01, a permanent beam will likely need footer support under your slab, because 2 beam supports represent 2 point loads that a 3" slab is not rated to support.
You would do well to research beam design and estimate loading, make a sketch and talk to an inspector about your design. Most inspectors I know will honor your research and give you general advice. Specific advice will come once you submit a permit request.