320 x 200 CGA allows you to have only 4 colors at a time. Of course you can change the fixed palette on a certain scanline to have more colors. See for example California Games.
Yes, I did consider writing "4 colors", but thought someone would say "but you could have 16 colors on-screen" citing the early 80s titles which did scanline palette tricks. So, I went with "16 colors" as it was technically the upper-bound of 'official' documented colors (excluding composite artifact, dithering and other cool tricks). I didn't really want to get into explaining more since my goal was just linking the "8088 MPH" demo for the GP and anyone who hadn't seen it. Also, I have no idea if a technically correct, definitive and complete statement about CGA's maximum possible colors in a single English-language sentence is even possible.
But after wasting... oh, nearly ~800ms on this internal debate, I realized I'd already cleverly chosen to not link directly to the 8088 MPH video but instead a site containing both the video and links to explications revealing the myriad brilliant tricks and unnatural acts behind 8088 MPH. And from that rabbit hole, one may learn more than any mortal should know about CGA graphics. Especially apropos since the author of the OP was instrumental in creating 8088 MPH (although the OP's post is about BIOS things).
Bah! You kids with your newfangled graphics modes. 320 x 200 CGA and 16 colors is more than enough. See the linked "8088 MPH" video for proof: https://trixter.oldskool.org/2015/04/07/8088-mph-we-break-al...