You can relinearize to your heart’s content, but you are unlikely to improve upon the first one in my experience. I’m a little obsessive about trying to attain perfect linearization, but over the last 2 years of working with PiezoDN I have come to realize that with all the sources of variation in the printing system (I mean in the darkroom, not making the negatives) such as slight variations in coating or fluctuation in exposure light output, that doing so is an exercise in futility.
I think the best practice would actually be, rather than rely on a single print of the target negative, to print it several times and average the results, then use that to make the linearization, and do the same to verify the linearized quad. Most of us, me included, don’t want to do that because it is so time consuming, but in the end it may actually save time. This is just a recent thought - I haven’t put it into practice - yet.
Here’s an example where I made 3 iterative linearizations:
In the end, I have chosen to use the first linearization because I like the way it looks in actual prints. The others look too dark, especially in the highlights. I suspect that there was a fluctuation in exposure light output that resulted in a target print that appears to be too light, but that if I reprinted it a few times and averaged the results I would find it was an outlier.