Hmmmm ... I'm not sure how you're doing the programs. For myself, I'm using weights that take me to failure by the end of each set. That is, by the last rep I couldn't do one more with proper form. There's been some trial and error finding that perfect weight. Even with the 1 RM testing, I've still needed to fiddle a little. But if I "miss" on a given exercise, I'll adjust my weight, go back and ace it.
This is my second time through STS. The first time, I did the 5 1/2 mo. rotation. I'm going with the undulating periodization approach this time (and really enjoying it). Anyhow, really zeroing in on the correct weights to give 100% in every set, I can't really see any reason to do the workout twice. Cathe did such a phenomenal job designing these workouts, they are "just right" as is and need no additions or "improvements." My opinion, of course.
To think of it, my first time through STS I was really glad I'd opted to do the 5 1/2 month option. Sometimes the first time through a workout there was a learning curve (for lack of a better term). This especially in meso 1. With the pace and equipment changes I felt sort of scattered and was glad I'd get a second shot at the workout to really nail it. If this is at all what you're experiencing, you might consider the longer rotation. It can be hard for me reel in my enthusiasm. I have to remind myself that I'm in this for the long haul and sometimes enough really is enough. If I overtrain or end up injured, I may not be able to do "squat (that, quite literally)".
Again, if you've really chosen the correct weights, I'd think your muscles would be adequately (to say the least) worked. Particularily in meso 2 and 3 (with the heavier weights) and repeating the workouts would just be overkill. More than what they offer might actually bring diminishing returns. If you're really jazzed for a second workout and just gotta do something, I'd go for cardio.
You could post this in the "Ask Cathe" forum if you want her expert opinion on this, of course.
HTH,
My Best To You,
Lori