Mine usually bloom late may to early june. I'm not sure how much that varies from state/zone to state/zone.

Here the native dogwoods bloom in May but my Kousa dogwood blooms in mid-late June - it still has some blooms now. Are you trying to add more spring bloom or spread out the bloom season? For a nice late summer blooming small tree, try a heptacodium. Mine blooms in late September.

Kousa blooms 2-3 weeks after native dogwood

Mine bloomed the middle of June last year. Variety 'Satomi'.

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Cripes, someone with a 'Satomi' that actually blooms!

The popular C. kousa and forida hybirds bloom earlier than the kousa species.

A 'Satomi' that blooms pink! Mine always blooms, but unless its a cool spring right up to bloom time, its usually white with pink edges, or maybe pink bleeding is more accurate. In the 11 years I've had mine I'd say only 3 years were solid pink years.

tj