Well, I'd like to take things one step at a time. The Doctor does actually sometimes have more than one companion , though there still usually tends to be a "mane" companion, one that joins first and is more focused on than the others. For example, the Doctor met a girl named Rose in the first season and then she became his companion. Then a few episodes later, Rose's boyfriend Mickey started to become more and more relevant to the story until he started tagging along as well and became a secondary companion
In other words, I like the idea of having more than one companion, but I'd rather that happen later on