What you need is a process called "underpinning", and any good concrete or masonry contractor should know how to do it. Basically what they do is remove a small section of soil below your foundation wall (two or three feet at most) and fill it with concrete from the bottom of the existing foundation to 8 inches below the new basement floor level. They do alternating sections, leaving twice the width of the dug-out part between excavations.
Your support posts need to have new footings below the new basement floor, and the posts themselves need to be replaced. What they will do is install temporary posts on each side of the existing posts, maybe 3 feet away, and then remove the posts, footings, and soil, down to 8 inches below the new basement floor.
Then they will pour new footings, and replace the posts with new posts.
Other than maybe some leveling, you won't need to replace the beam, unless it is damaged somehow. If the outside walls have settled, you may need to jack the house up to level it, which can be done after the underpinning is in to stabilize the foundation.
It sounds more complicated than it is, but it is labor-intensive, and therefore a bit expensive.
Architect (NY) and Home Designer (PA)