I am currently schedule to sit for the Level 2 exam in November 2021. To hedge my bets on whether I pass, am I allowed to enroll in the February Level 2 exam before I have taken the November exam (ie: be enrolled in both simultaneously)?

Definitely not. Your next eligible date for CFA Level 2 is May 2022, and you can't register for a new exam until the results of your current exam is out, or if you withdraw beforehand.