You can change your plan at any time from Settings → Billing, via the "Manage Billing" button — this opens Stripe's secure billing portal, where you can switch plans directly.
Once you've picked a new plan in the portal, Stripe handles the proration automatically — you're charged or credited for the difference in your current billing period.
You can't start a second checkout in-app once you already have an active plan — all plan changes go through this same billing portal.