There have been several threads about this topic.... in my opinion, a properly installed, inside-tire patch for a tiny puncture in the tread area is just as safe as having had no hole at all. A shop that refuses to patch is a shop that just wants to sell new tires.... they can claim "liability" or whatever they want, and I don't believe it. It is the same nonsense about not mounting tires you didn't buy from them.
And there is also no logic in the shop saying they only allow one patch. It shouldn't matter if it is one patch or six... as long as they are not near each other or overlapping. Again, they probably just want to force you to buy a new tire.
Plugging is a different topic completely... I am less confident about plugs, although many here think, if done properly (and with glue), a plug will be perfectly safe and will last the life of the tire.