Yes. But the steel columns supporting the cut sections of the I-Beam have to sit on piers requiring you to break the concrete, excavate for piers, install rebar and pour.

The whole thing should be speced by a structural engineer and in most jurisdictions approved by the local building authority.

You might want to rethink the stair relocation.

Worthy's comments about cutting and patching the existing beam may or may not be possible. The steel beam is supporting something (or lots of somethings) on the floors above and carrying the load down to the foundation. Cutting the steel beam, supporting the cut ends with new columns and footings (and reconfiguring whatever the beam is supporting where it's cut) depends entirely on what sort of load(s) and where they are located for the steel beam.

For example, if the steel beam is carrying the distributed load of the floor joists above, one can't simply cut the beam for a 4' width for stairs. What do you think happens to those floor joists that were being supported where the beam was cut and removed?

Worthy is absolutely correct in recommending doing nothing before a structural engineer looks at and calculates everything.

I certainly agree: easiest and possibly best solutions is to find another location for the stair and leave the beam alone unless you want to spend what it takes to investigate, redesign and reconfigure the beam, new supporting columns and footings.

Good luck on your project.