I'd try swapping a TV that receives all the channels for the one that's having a problem to see if the symptoms are the same. Unless the problem TV has a very long cable compared to all the others it's unlikely another amplifier will do anything.
Yes it is in fact possibleIn my current setup, I have the antenna on the 2nd Floor attached to an 8 port amplifier which works great for most of the TVs. We have one television which isn't pulling in some of the channels the other TVs get and I'm trying to remedy the situation. Would a 2nd amplifier, used for this TV only be a possible solution?