No, and it's better if you don't. Enroll in your new plan first so you don't end up with a gap in coverage. Your current plan stays active through the end of the month before your new coverage starts, and Thatch updates your coverage dates so the two line up.
If your new plan happens to be with the same insurance company you have now, there's nothing to cancel at all. We'll handle it as a plan change.
There is one step that has to come from you. Because you're the policyholder, your insurance company can only accept a cancellation request from you, not from Thatch or your employer.
Once your new plan is submitted, you'll see a to-do on your Thatch dashboard named "Cancel your [insurance company] coverage" with the exact end date to request.
Call the number on the back of your member ID card, ask to cancel effective that date, and request written confirmation.
UnitedHealthcare is the exception: they only accept cancellations by fax or letter, and the to-do links to a template you can use.