Sounds like you're in for a complete rebuild - a piece at a time.
You will need a long range plan based on knowledge of existing
conditions.
Check soils. "Near a river" suggests high water table & poor bearing
values.
Check foundation of addition & compare with foundation of earlier work.
Plan on new continuous footings.

Jack up early construction to match newer.
Bring through beams to a fraction of an inch lower than "good"
construction.
Raise the rest of the through beam a bit at a time to lift entire house
to same level.
TB