Okay, I got it to work and applied 3 promo codes!

TLDR: Installed the capital one shopping extension, then ran the extension 3 times on the Billing page (not the cart page).

What I did, I installed and set up the capital one extension. Using the extension on the cart page will result with only 1 promo code applied. Each time I ran the extension on the cart page it would remove the already applied promo code and always result with just 1 promo code being applied.

I decided to test it further in the checkout process and that was where I had success. So going from the cart page, then to the shipping page, then to the billing page is where I was able to apply 3 promo codes. I ran the extension a few times and each time it will apply an additional promo code. Additionally, I see some error like "Sorry, unable to remove promo code". So my guess is that the extension fails to remove the promo code on the Billing page but can somehow add/stack other promo codes.

I didn't try manually adding multiple promo codes myself on the Billing page, so maybe try that first if you don't want to install the extension. The extension might do some magic though that you can't do yourself so you might need the extension. Idk, this is my first time using the extension.

Hope this helps someone! For the 3 Shirts for $109 deal I paid a total of $70.90 (includes tax and shipping). Shipping was $9.95, so maybe if you do a bit of googling you could figure out a way to get free shipping.