Answer: Transplanting your spirea can be done now, but I'd wait on the peony until after frost kills back the tops of the plant. That will signal the roots to go into dormancy. Once they're dormant you can move them without problem. If you dig and transplant now you'll interrupt the process and your peony may sulk for 2-3 years. Be sure to replant at the same depth as it was previously growing; planting too deep will keep it from flowering.
Best wishes with your garden!
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