My gut answer to this question is "no." Certainly, from a technical standpoint you cannot be a resident of two different states simultaneously. There may be a way to exploit the fact that there are two different application systems, but I doubt it.
When you claim Texas residency through TMDSAS, you need to actually submit a residency questionairre, and basically argue your case for being listed as a Texas resident based on things like voter registration, driver's license, motor vehicle registration, land ownership, etc.
You'll need to read the guidlines for each individual state/school regarding your residence. I was thinking of doing this with Iowa and Texas--Iowa being my permanent home and Texas being where I work. However, Iowa does not allow you to be a resident of two states and from what I know TX will deny residence if there is any uncertianty.