Is the "level" off because of sagging in the joists?
Pay careful attention to WHY they are sagging. Approach a sagging floor from an engineers point of view..... if you shore up one part of the floor the weight still has to be transferred down into the foundation... by re-enforcing it just by blocking you may be transferring the load to another portion and it may not be designed to carry the load.
Example:
A floor joist is sagging due to not being "Large" enough to carry a load. The load is dead in the middle of the floor. You go to "shore it up" but you end up transferring the weight to ONE side more than the other and it's the weaker side. You've actually created a problem instead of fixing it.
Just be careful
