Lindens are prone to suckering. Stress will make many trees sucker, and will probably increase suckering of lindens, but, well, lindens are likely to sucker even if they are healthy and happy.

To the best of my knowledge, all you can do is make sure that the mulch doesn't touch the base of the tree, and remove the suckers promptly. They'll probably come back no matter what you do.

Yes we have them round here with suckers(we call them Lime trees) and apparently its because they are hybrids-usually Tillia x europea. True species(T.cordata etc) don't sucker.

Maybe it's a silver linden, they are supposed to be more prone to suckering.

Greenlarry has it - it is Tilia à europaea that suckers freely. The other species don't do this, but are often grafted on Tilia à europaea rootstocks, because this is so easy and cheap to propagate from root cuttings.

The different leaf shape between your tree and its suckers suggests it could well be a grafted plant.

Resin

OP didn't state different leaf shape, just larger leaves. Sucker shoots tend to have bigger leaves because of their vigor. Tilia americana is also another species that is usually seen with 5 or more suckers at the base. And yes, the tree will probably be still suckering long after you are dead.

Thank you all for the information. I guess I will just try and keep up on removal of the suckers as best I can.

Thanks again!