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Yes, they (paid plans) all do.
Actually the free plan is the only one that differentiates between the plain submissions, secure submissions and paid submissions.
When subscribed to a paid plan, you can have any type of submissions made in the amount of submissions allowed for the account - meaning that you can have any type of submissions made, up to 1.000 for Premium plan, 10.000 for Economy and 100.000 for Professional plan.
So for paid accounts only limit is the total number of submissions per month.