Maxwell – Max for short – was twice offered a chance to travel with the Doctor in his TARDIS. He refused both times, preferring instead to run the Stockbridge Division of the Bureau for Interplanetary Liaison, a group of people extending a welcoming hand to visiting aliens. He was, in essence, the Stockbridge "UFO chaser", viewed by his neighbours as a crackpot.
Practically the only resident of Stockbridge who believed in his cause was Izzy Sinclair, who joined his organisation. It was through Max that Izzy was introduced to the Eighth Doctor and became one of his longest-serving companions. (COMIC: Endgame)
Although (originally) a comics-only character, Max had a certain degree of commonality with the televised character of Wilfred Mott. and is given a very similar personality when the character was adapted for audio while Wilfred was appearing. Given Russell T Davies' stated affection for the Eighth Doctor comic strip, it's entirely possible that he served as a sort of springboard for Wilf.
Max may not qualify as a "companion", though his multiple appearances exceed those of many characters considered to be companions, such as one-offs Astrid Peth and Adelaide Brooke.