One of the revolutionary things about tulips at that time was that the unique patterns caused by https://en.wikipedia.org/wiki/Tulip-breaking_virus were only partially inherited: after a few generations, the bulbs are too weakened to survive, and the particular pattern disappears permanently, no matter how lovely and beautiful it was.
If you read up on a book about Tulipomania, you'll notice there are no contemporary photos of tulips like Semper Augustus. Because Semper Augustus no longer exists.
So you can 'plant new tulips at will' the same way you can 'paint new Rembrandts at will' ie. slap some paint on a canvas and hope it looks vaguely similar and that's the best you can do, since you can never ever get another real Rembrandt or real Semper Augustus.