The answer to your question is no, the parole board cannot extend your parole beyond the total length of the sentence. Now to explain what they've done to give you this appearance you need to answer the questions that everyone has already asked you several times. I have represented people in parole hearings and I have no idea what you are talking about when you say they are taking away flat time. That is not how parole works. As stated above, you get sentenced to a term of confinement and that is the max time you owe on that conviction. You can serve that time in prison or on parole. You can be released early from parole but it can never be extended beyond this max term. What the parole board CAN do however is control when you START serving that parole...as I'll explain below.
Parole law is complicated and you have not told us the whole story. You need to tell us all offenses you were convicted of in 1983 and the exact date of your sentence. Was it May 29th 1983?
The way you talk about them adding time for a previous violation makes it sound like you were still serving out a parole for another offense at the time you were convicted in 1983. You need to tell us what these conviction(s) were and when your parole on them was to expire.
My guess is that you have multiple sentences that are getting stacked for one reason or another. If you were convicted of two offenses in 1983 they could have been stacked against each other, or if you were just convicted of the one offense, it could have been stacked on top of whatever offense you were still on parole for. There are all kinds of weird nuances in the Tx. parole system that can create weird stacking sentences, like if your prior charge was a possession charge in a drug free zone, that automatically stacks half of the sentence on top of anything you pick up later. The bottom line is that it sounds like the parole board did not extend your parole term, they simply suspended the date that you started serving that parole, because you still owed time on your prior parole. I can tell you how to verify that the parole is calculating your days correctly, but first you've got to give us more details.