Conversation so far:
Where does Andy pick up in season 4?
The fourth-season premiere, "Fun Run", has Andy competitively participating in Michael's superfluously named run for rabies prevention through strategically drafting Kevin, although he falls prey to "nipple chafing..
Does he have any rivalries with Dwight?
Dwight uses pressuring negotiation tactics in order to buy Andy's Nissan Xterra at a reduced price, only to flip it for profit on eBay much to Andy's protest.
Does Andy get revenge?
CANNOTANSWER.
Are there any other rivalries going on?
Jim reveals Andy was invited in order to benefit Jim, as Andy's pride for Cornell would push the client- a graduate of Dartmouth- toward him.
How did Andy react?
The scheme plays out as intended when the client invites Kevin to play golf with him again but denies Andy's request to join them.
How does that work out for the company?
CANNOTANSWER.

Question: What other interesting events have they had?
Self-contained rewrite: Besides the rivalry, what other interesting events have Andy, Jim and Dwight had?