No, I don't believe it is possible to be two types at the same time, and it would actually be unnecessary. We are not limited to only our top two functions, I feel that is a misconception in MBTI practice. For instance a person will be seen as articulate, or Directive, and then automatically be thought of as an Extrovert or a J. But it is not how much one can speak that makes them an extrovert, and it is not the ability to be directive that makes one a J, because we essentially all have this ability. In that same regard, an INFJ is not confined to Fe judgment, they can, and do modulate to Ti in order to also use a form of judgment based on personal logic. Therefore it is entirely possible to have an INFJ that has well developed Ti, however this does not make them an INTJ as well. The INFJ consciously uses Ni-Fe and Ti-Se, while the INTJ consciously uses Ni-Te and Fi-Se. The worldview and identity that Ni-Fe creates for the INFJ is significantly different than the worldview Ni-Te creates for an INTJ. So while being more than one type is not possible, it should not be considered a limitation per se, because we still have the ability to develop our other functions and adapt when neccesary. There difference is that as an INFJ, you begin with Ni-Fe and spread out to other function, while the INTJ begins with Ni-Te, and spreads out to their other functions from that "launch point."
The MBTI test is technically only checking for proficiency in your top two functions, and the descriptions are only describing a person that has proficient use of their top two function. That means that a person who has developed more than their Top two functions will more than likely test as something else, and they will contradict as well as not relate to the descriptions of types.
When a person begins to develop their lower functions, you will begin to become more consciously aware of these functions, and they actually become closer to one's identity. This shifts your perception of what you are, and what you are not (The ego and the Shadow if you will). For example, in the case of those INFJs that have very well developed Ti, they tend to consider their logical side a very strong part of their identity. So much that they are insulted that I might suggest that they are in fact feelers.
Hahaha, yes, totally! Actually almost every person I meet, I generally do it only if they are more than just a random encounter, or if I feel a certain magnetic pull that person and want to explore why I am subconsciously liking them.