replace beam to level the floor?

[Medi]

Hi all, I need a good advise on the best way to fix a sagging floor, the problem in my old house is the floor sags in length and width of the space.
This is a 1940s cape cod that was upgraded and expanded to add space so they expanded the master bedroom room on 2nd floor out beyond the exterior wall and added columns to support it. I attached the plans for it, the little double lines are the doorways and there is a stairway next to the master bedroom. There are also walls that have no support from underneath and add weight to the floor. The living room width on level below is from stairs to exterior wall. Currently I removed the floor in both bedrooms to expose the joists.
Here is the issues: there is a "beam" at about mid point of my living room which is below the two bedrooms above. The beam protrudes down about 9" from the ceiling of the living room and supports the joists for the two bedrooms above. I assumed it's 10" because there are two layers of Sheetrock ceiling. and actually the "beam" is 3 joists sistered together, most likely with nails. The beam sags about 2" at midpoint and the joists from both sides are sistered together at the ends and sag pretty good as well.
after much online research I've figured I can do it two ways:
1. sister each new joists slightly higher as I move from exterior wall towards the middle of the room, to compensate for the sag in the "beam"
2. replace the beam with i joists. maybe install two of them in parallel, cut the ends of the joist and level the new i joist to the same elevation, this way it eliminates the protrusion from the living room ceiling and helps me clear the beam with my head since the ceilings are low - 8'. In this scenario I would also sister new joists to treat the sag along the length of the living room.
another trick I was considering is using the dividing wall between the rooms as another support for the joist by sliding an edge of plywood under the wall and putting 1.25" screw (because I have only 7" space to get the drill in) into the wall sil from underneath and then putting long screw through plywood and joist from the top on both sides of the wall. Will this actually work or will it end up pulling the wall down with the rest of the floor when it settles?
my main concerns is by sistering joists i will be adding weight and the beam might sag even more.
Let me know what you all think is my best option. I don't mind going the hard way as long as I get the optimum result which is leveled floor.

[Kelly_Bramble]

I would suggest a review by a local engineer to ensure that the structure meets local codes and is structurally sound in the first place.

In absence of a local engineering review I would consider adding column supports under the separating walls to distribute the loading. There should always have been structural support under heavy wall or any structural sections.

Without see the sagging joists it can be difficult to understand is replacement or sistering is the right solution.