I will try to answer, if no onechimes in

Have not done it myself,
If you mean Alyssum montanum or A saxatile, that is not exactly a perennial but rather a subshrub, like Rosemary or Lavander. Those transplant really badly when very old, how long is yours on its present spot?

If, then I would move it after flowering, clipp back sharp, and replant. And if it is older than 5 y, I would try to start cuttings.

Hope that helps, bye, Lin

Thanks for your answer Lin! Yes this is Basket of Gold, Gold Dust (Aurinia saxatilis). I winter sowed them and some have been in ground one full year, others for two years. I thought perhaps I could move them this early fall as I think I would like them in a better location. (mass planting) But I have read two different articles saying they don't like being moved. Perhaps I better leave them alone. :)