Theoretically speaking, how long would the human lifespan increase if it
were possible to replace all of our internal organs?

Excluding the exponential number of unknowns which render your
question virtually unanswerable, your question has several fundamental
problems. Here are a couple:

1) The timing of the "operation" would impact the percentage of
increase in the patient's life. For example, if the replacement was
done at age 20, the lifespan might increase only 30%. If the
replacement was done at 80 the increase might represent 90%. See what
I mean?

2) Assuming that this replacement of "internal organs" also includes
the brain, the recipient will effectively die upon the removal of the
brain and the replacement (which we will agree for the purposes of
your question, will be successful) will result in a new brain, which
in turn will create a new person and a new life. Given this scenario,
the increase in lifespan of the original recipient is 0% and the end
result is the Mary-Shelleyesque construction of a new person using
both new and used dismembered (and thereby "unliving") body parts.

Heady concept, isn't it?

tutuzdad-ga

Interesting Question;

It would still be limited by degredation of telomeres, polynucleotide
repeates at the ends of each chromosome which prevent loss of genomic
material in successive rounds of replication. Shortening of telomeres
is associated with aging - as chromosomes are replicated, and
telomeres shorten, eventually damage is sustained to functionally
relevant areas of chromosome, which may result in apoptotic cell
death, or in other cases, cancers.

Larry Niven discussed this in some of his books and short stories. Good reading.

The point I'd like to add is that replacing the internal organs does
nothing to combat the osteoporosis and sarcopenia that accompany
normal ageing in the parts you aren't changing (bones and muscle) - so
even if you did manage to increase lifespan (by somehow successfully
carrying out such a huge operation...) then you're going to be living
for a longer time, but with reduced quality of life. Not sure if I'd
be up for that...

This may be off the internal organs, but to just take out your brain,
and insert it into a newer younger body would extend your life the
longest.  From what I understand Telomeres Therapy may be available
some day that would slow down the ageing, somewhere to how they were
in the bible; men living to be 1000 years old.

     With the first senario I would suppose you could live forever,
yet eventually with old age your brain would deteriorate so badly you
would become a vegtable.  Last if you found some way to take the
electrical impulses from the brain and transfer them to a new brain or
even a machine, well "ghost in the machine" I guess you live forever,
or until someone pulls the plug.  With new science capabilities it is
also now possible to regrow your own organs using your stem cells/dna,
the idea of replacing most of your internal organs to live longer is
more likely because of less rejection by your body, the idea may not
be that far fetched.  In response to your question you could only live
as long as your cells continue to divide, if hayflick is right you
won't live past 120 no matter what you do.