You can graft over them. The rule is try to graft twice, if it fails a second time, get rid of the rootstock. Just pick one sprout on each rootstock and rub off the rest. By this fall, you should have some nice rootstock specimens to graft the following spring.

I dunno about that two strikes & you're out rule; who invented that, the infamous 'they'?
I'd have thrown away a LOT of pecan and walnut rootstock in my day if I had to discard them after two failures.
With pears, you'd really have to botch the job not to get a 'take' - I kid when I say you can just throw pear scions at the rootstock and they'll take - but it's not much of an exaggeration.
Actually, you could probably select and promote a single vigorous rootstock sprout and bud onto it this summer - or wait 'til next spring. Whatever floats your boat.

Lucky,

I've read commercial nurseries discard the rootstock after two strikes. After two strikes the likely hood of successful takes decreases significantly. Failure is attributed to virus load. Not sure the rule applies to nuts, since they are harder to graft to begin with, and one would expect more failures. That said, there is nothing to keep the backyard grower from trying to graft a rootstock as many times as he/she likes, provided there is an ample supply of scionwood.

Gotcha. I'll buy that one, olpea.
In a commercial setting, with virus-free rootstock and scionwood of unknown viral-infection status, I might go along with the 'two strikes' rule, but for a couple of rootstocks in my orchard or hobby nursery, I might try more than twice, if I were unlucky enough not to succeed right out of the gate.

Guess I will let the suckets grow and possibly try for a graft next winter/spring. Thanks.

If you want to let two-three-four suckers grow you have multiple chances. You might want to use one or two of them to try budding this summer. You would have to find budding sticks in August (dormant buds on this year's growth), but that's doable, I would think. Once the bud healed in you would be ready to force it in the spring. If that bud were rejected you'd be able to try again in the spring anyway.

Good luck,

M

A couple of years back, fireblight killed my Korean Giant all the way to the ground, and the Harbin pear (P.ussuriensis) rootstock threw up several suckers; I let 'em all grow. Last spring, I pulled all but the largest/most vigorous off the stump - some with roots attached, and stuck them in a plant bed. 50% rooted and have leafed out this spring, so I'l be grafting something onto them this weekend.
Never got to regraft the big, vigorous sucker as it was in the area of the orchard that my wife bulldozed to put in a tennis court.