system
Given the following post, respond as if you're commenting on Reddit:
human
You get a donor organ or tissue from a stranger and after natural cell-decay your body renews the cells; then which DNA will be in the new cells?

Stated differently: how long is an implanted donor organ recognisable as foreign tissue? Will it ever be made with your DNA or is it the donor's forever?

And what would change if it was a different organ or tissue? 

You can take it further: how much different DNA 'sets' can there theoretically be 'active' in a single human besides the original?
gpt
It is forever the donor's organ, with the donors DNA.  It will never flip to become "yours", so you will have to take drugs for the rest of your life to prevent rejection of the organ by your immune system.

Many DNA sets within the same individual are possible, the problem is with tissue rejection.  If you're interested, look up somatic mosaicism, where it's possible that normal individuals have separate DNA sequences in different cells of their body.