I asked Lucina what happens with MTP+FaT. The response:
Lucina wrote:
I believe the framed person would only show up guilty if they were investigated by Gay Knight, Police Officer Clues, or Mayoral clues (basically something that wouldn't make investigations with clues they picked up at the kill site)
So MTP only affects clues taken from the kill site, and overrides FaT, which affects all investigations.
We can tell whether mafia used MTP+FaT+FaT vs FaT+FaT by having mayor investigate. (This is probably a waste)