Here's my take.
MBA
If you have pressed the elevator button, regardless of if you pressed up or down, they must press the button they want to go in again. It's as if pressing the button will somehow, as if magically, send a signal to the elevator controller to send it in their direction faster. I believe this is their way of exhibiting dominance over something just like they will over people when they leave school. Think "selfish CEO".
When the elevator door opens they will simply enter it regardless of the people that are exiting. They typically do not say "excuse me" unless there are multiple people exiting. It's as if the other people are in their way, they are not saying that to be polite, they are saying it as if "you're in my way, move". Basic social politeness rules are simply not present in the MBA type. I mean why should there be? With what they pay in tuition right?
Now, if you happen to be in the elevator when they arrive after the "excuse me" part, they nearly universally ask "which way is this going". This is always regardless of the large LED display panel planted squarely in front of them with a big arrow that points either up or down depending on the direction the elevator is traveling. Now, granted outside the elevator is yet another large LED indicator that showed them the direction of travel prior to entering the elevator. But, that's 10 seconds in the past and they haven't taken the optional "self reflection" course in their time at school. We all know anything beyond 30 seconds is just too difficult to remember. This is the same reason all financial bubbles happen, the previous one was beyond 30 seconds in the past.
When the elevator door finally opens to their destination they exit as quickly as possible, usually before the doors even open all the way. If another MBA is trying to enter (remember the "excuse me" from above), they will simply exit through the excuse me. If there are multiple MBA's trying to exit at the same time, they will all try to do just that, exit at the same time. It's as if the first one through the door "wins" in some way, I suppose this is the same hyper-competitiveness they exhibit in class and throughout life. I mean really, if you don't make it through the elevator door first how could you EVER get that promotion?
PhD
This species is similar to, but in other ways, unique from that the MBA species. They exhibit the same signs of impatience, selfishness and rudeness however they take that to an extreme and add in a healthy dose of anxiety.
For example, while awaiting the elevator they will again press the button that's already been selected, the difference is they press it several times. Many, (many) several times. It appears they are, in some way, hoping that button has some ethereal power to help them get their PhD faster.
While in the elevator they often show intense anxiety, often pacing and many times running straight into others. Many times this is coupled with a press of the button for the floor they are going to every time they complete a loop in that anxious pacing circle.
Faculty
Ok, here's where it's starts getting interesting, especially trying to distinguish between a PhD and Faculty. Faculty do in fact exhibit the traits of a PhD, as well as many of the MBA, however they often exhibit additional bits.
First, their patience level is that of a 3 year old.
Staff
These are the easiest to spot as they're typically the opposite of everything above. Not only do they wait to get in the elevator, many times they will have identified the affiliation of those already in it when the doors open. If they spot, say more than 50%, of the previously mentioned types in the elevator this species will simply say "I'll take the next one, I don't really want to go to work anyways".
Once in the elevator they will quickly identify you as "one of them" and open a dialog, often starting with the weather and given this is Chicago, it's usually crappy weather. They're often pleasant types, especially to you, since you're from the same planet they're from. Many times they won't remember to push the button for their own floor and if you exit before them they will say "oops, I didn't really want to go to work anyways. I suppose I'll ride it back to the basement and up".
Exiting the elevator is the precise opposite of all the types above, they will nealy universally let you exit first which usually accompanies the words" I don't really want to go to work anyways".
Alumni
These are rather difficult to spot in the wild, why would any self-respecting alumni be located back on campus? Of those that I have seen they tend to be the exact opposite of all the traits above and quite often resemble humans.