My Sophomore Track season I ran 52/2:00/4:36. This past cross country season I ran 16:30 for 5k. If I were to tempo run 4 days a week, leaving 3 for recovery, would I turn into an absolute beast, and improve on these times? Or would I demolish myself?
It depends on a lot of factors. If you dropped from 80 miles a week to 50 and did 4 tempos a week, you'd probably be fine. I doubt it'd be the best way to train, though. If you kept your milage the same, youd probably get injured or get slower
The issue isn't really that you would demolish yourself; it's that your training would be one dimensional and you would be forgoing a lot of other necessary work to do your tempos. You could really run a tempo every day if you wanted to and you weren't doing any hard workouts, but that wouldn't really be good training.
You could go every other day, which would work out to 3 or 4 per week, depending on the schedule. While this will work your aerobic fitness, you won't get top end speed, which you'll need when you peak.
The only way to find out is to do it. I know a guy that tempoed 10 a day. Eventually he shredded his Achilles, but he could beat everyone in town.