My department promised graduate students a particular teaching load, but has found a loophole to increase it I am a second year STEM PhD student at a large R1 public university in the United States. When I chose to come to this program, the department told me that I would have a teaching load of 3 classes per year. That is, I would be expected to teach two classes in one semester, and one class in the other semester per academic year. The language in our contracts is not in terms of classes taught or credits taught, but a vague statement to the effect of "teaching xx hours per week". Since a statement in terms of hours per week is obviously vague, I inquired about this when I choose to come to this program, it was explained to me that it was simply 3 classes per year and that the load is not as high as it seems on paper. Other graduate students had the same experience. 

Now, they have changed their promise and are now expecting me, and some other graduate students as well, to teach four classes per year. We are upset about this because we feel as if the department intentionally misled us with the language of the contract. Since the department is not increasing our stipends, we also feel they are exploiting our cheap labor. This has also led to resentment among graduate students since some did not get chosen to teach extra classes, and it was essentially random who got stuck with a higher teaching load. 

My question is: Is it reasonable to ask the department to increase our stipend or compensation for this additional work? If it isn't, what is reasonable to ask of them? Should we just get over it?
I think this is unfair, but there is probably nothing that you can do about it.  In my STEM department, TAs all nominally are responsible for the same number of work hours (twenty hours per week), but with different courses and different grading responsibilities, it is inevitable that there will be some iniquities—including some students teaching more sections that others.  Sometimes students unfortunately get saddled with extra work unexpectedly.  Mostly, the students grin and bear it, knowing that we try to have the extra work average out over time (see below).

As a practical matter, funding for teaching assistantships at an R1 institution mostly comes from outside the department (probably from the dean's office).  There is a set number of fully-supported TA slots available, and the department has a certain number of courses that it needs to have covered.  There may be a bit of extra money in the departmental budget, but if the department suddenly and unexpectedly increased the teaching load for some of its TAs, that suggests that the department may be in a precarious financial position, with little to no extra money available to support the TAs who are working harder.

It will not hurt to ask for additional money.  However, even if there was enough money to pay the overloaded TAs a bit extra, the department would probably say no.  If they did start paying some TAs more than others, that could provoke even more ill will and dissension among the graduate students; the ones who were not assigned extra sections would be (quite reasonably) angry that they were not getting the same opportunity to make extra money as some of their fellows.

So, I think it is quite unlikely that you will get any extra funding for teaching one extra class section per year.  What you can realistically ask for is to have the extra teaching load spread around between different TAs; this year, maybe half the TAs have to duty extra duty, but next year, those additional courses will fall on the shoulders of the other half.  The department may already have it in mind to do this, but it would not be a bad idea to get it stated as an official policy goal to handle things this way.

One final thing that might be relevant.  The amount of teaching that faculty members do in R1 STEM departments is far from uniform.  In biology, chemistry, and physics, full load for professors is typically teaching one or one-and-a-half courses per semester.  In other STEM areas (geology, mathematics, neuroscience, etc.), the course load for faculty can be about twice that.  That means that different kinds of STEM departments have different amounts of slack in what the faculty are available to teach.  Depending on your field (and the local departmental culture), it might or might not be viable to have professors take up some of the extra course responsibilities.  It is too late for that to change for this semester and maybe the next semester too, but things might be different next academic year.  (Again, however, this is probably something that the departmental faculty have already thought about and discussed, so any complaint you make is unlikely to make a great deal of difference in what ultimately happens.)