If you can do 3 pullups at 290 pounds, you are very strong already. I can do 12 at 205, and I know at 210 I can only do 10 and at 195 I can do 16. Actually I think it is more a function of body fat precentage than actual body weight.
Other than that, the best way to increase pullups is to do pullups. You can try doing negatives (fast up and 30-60 second lowering), assisted pullups (on machine or with bands), weighted pullup negatives, pyramids (1 pullup, rest 60 seconds, 2 pullups, rest 60 seconds, 3 pullups, rest 60 seconds, 2 pullups, rest 60 seconds, 1 pullup, next exercise session try to reduce rest periods by 5 seconds), do sets of 1 or 2 reps every 30 seconds until you complete a fixed number (20?) of total pullups... there are many varieties of pullup schemes, designed to produce a significant volume which might increase endurance and strength.
You might also try a pre-exhaustion scheme by following a set of pullups with a set of curls, lat pulldowns, bent rows or some other movement that works some or all of the same muscles. Or superset pullups with a pushing exercise, like bench press or military press. Of try fartlick training (do a set of pullups, run 1/4 mile, do a set of pushups, run a 1/4 mile, repeat that sequence 6-8 times).