The CAA rate uses the exact same rate code as the AAA rate in the Marriott system. The following page on the Marriott site is references CAA Member rates. You can see that the promo code (which is automatically populated by the website) is AAA.

https://hotel-deals.marriott.com/canada-caa-rates/

Additionally, the AAA Hotel Discount page on the website includes the following text in the Terms and Conditions: "Limit of 2 rooms per AAA/CAA member per night".

https://www.marriott.com/hotel-discount/aaa.mi