If you leave the side shoots you'll get smaller flower spikes from them as well as the main spike. I leave them myself. Also remember foxgloves are biennials, so if you want to grow more let a couple of them go to seed; pick ones that are as inconspicuous as you can, they're not pretty in seed, let them get all brown and dry, then shake the seeds where you want the babies next year. They come up as fuzzy little rosettes, and may or may not bloom for a year. Ours are from some wild ones growing on our property, and I have lots of little babies wherever I shake seeds. Mine are all shades from purple to white.

The flowers open from bottom to top of the long spike so there will be seeds forming at the bottom while the top is still flowering.

They grow taller in semi shade and among shrubs.

Sometimes, when the main spike and the side spikes have finished, the part that has flowered dies out and leaves 'pups' or rosettes around the dead part ready to start again next season. (This is so for Digitalis purpurea, I haven't had much joy with D ambigua :-( )

Seed will sprout in the late summer after the autumn rains and the young plants stay as little, flat plants to survive the winter. They need to fall on bare earth to succeed, rather than into leaf mould or litter.

If you have pot plants nearby - check for seedlings... As those long flower spikes move they can throw seed a long way.