Like many current NCAA athletes, I have the chance to use my extra eligibility in grad school. I'm not sure if I can move up divisions or not. I most likely won't, but I thought it would be interesting to see if it were possible through the NCAA rules.
And yes, I can obviously talk to my coach or other faculty about this but I thought this would be a nice first step!
You are certainly ALLOWED to. Whether the team at the D1 institution you go to for grad school has space on their team or wants you is a separate question. You should probably check with those coaches and that athletic department for specifics, as you'll only get general answers here.
The biggest thing would be your times and if they stack up. How fast have you run?
There is no rule against it.
I cannot see why not. Maybe ask your compliance officer since that person should know more than random, anonymous people on a message board.
Hard to believe it's been almost 20 years, but my team mate, who won a D3 5k championship, back then at a D3 school graduated with one year of XC eligibility left and got into the electrical engineering PhD program at a D1 school with a very good XC team. He raced for them and ran conference finals for them, which the team won.