I didn't know Friday built on other books. I tend to treat the books as stand-alone except for if they explicitly mention characters in other Heinlein I've read -- ie: Time Enough/Moon/Cat Who Walks.
I was editing my earlier post while you posted this. It's been a long time since I've read
Friday and
To Sail Beyond the Sunset, and I may have confused the characters Friday and Maureen Johnson, as I thought I remembered Pixel the cat in
Friday as well. I went back to my bookshelf and pulled out my copy of
Friday, and I could be wrong. I just know that I started reading Heinlein before he published
The Number of the Beast, and continued to read his books in the order they were published, and
Friday came out between
The Number of the Beast and
The Cat Who Walks Through Walls.