I'm currently a grad student in STEM in the US. I'm currently receiving a very modest stipend for acting as a TA, as well as getting credit for some research this semester. I'm also interested in doing some research not directly related to my degree for a professor in my department who has been publishing papers on another, tangentially-related subject.
Would it be normal/acceptable for me to ask for extra pay in return for working on my advisor's pet project, if he would benefit from the work of a research assistant? He's not asking me to anything I'm not getting credit for, I just had the idea that I might ask.
My current stipend isn't making ends meet, and, if I can't get a raise, I'm going to take a part-time job doing menial labor to avoid relying on loans. I don't mind the labor at all but spending the time working on research would be better for my career.
Whether this is acceptable or not will generally depend on whether the TA and RA are set up as "salaried" positions or as hourly positions, which can vary from institution to institution.
When set up as a salaried position, a TA or RA generally covers tuition and "living expenses," where that living expenses is a stipend intended to be sufficient to enable you to live somewhere nearby in a fairly sparse and monastic manner. In this case, you are expected to be acting as a full-time student, a significant part of whose time is spoken for by the TA or RA duties. In this case, it would not be appropriate to ask for a second TA or RA, because you are already being paid for your full expected working time.
When set up as an hourly position, on the other hand, the TA or RA is more of a "piecework" employment, where the school is only paying you for the particular hours you work, and taking no responsibility for ensuring that your pay can cover tuition and living expenses. In this case, it would be perfectly acceptable to combine this with another job, including another TA or RA.
If you are in the first case and you aren't being able to make ends meet, then you may need to adjust your lifestyle to meet the level of poverty that your institution expects of its students---or else find outside consulting work (if permitted) or organize for better wages.