Leodhas. Always Room for One More

Always Room for One More is a children's book by Sorche Nic Leodhas (LeClaire Gowans Alger), with art by Nonny Hogrogian, published in 1965; it was a Caldecott Medal winner for 1966. It is available at the Internet Archive.

Here is a YouTube read-along:

Like the Mitten story, this "room for one more" story is about squeezing into a small space: in this case, it's a Scottish couple with many children in a small house, but there's always room for one more. They are joined by a whole series of guests, and there's a folksong included in the back of the book in which the owner of the house sings to the passers-by that there's always room for one more:

Here's a YouTube with the song so you can sing along!

The story is not told cumulatively, but it would be fun if it were! Instead, all we get is a list of the people who squeeze into the house (with a glossary of the Scots words in the back):

A tinker came first, then a tailor,
And a sailor with line and lead;
A gallowglass and a fishing lass,
With a creel o' fish on her head;
A merry auld wife full o' banter,
Four peat-cutters up from the bog,
Piping Rury the Ranter,
And a shepherd laddie
Down from the brae,
With his canny wee shepherd dog.

Then, as they are dancing and having a wonderful time, the house falls apart... so the family builds an even bigger house. The father sings that "there's always room for one more," but of course there's no house big enough for all the people in the world, so another way to expand the story would be to add more people to the guests so that even the bigger house bursts too, but the father keeps singing, etc. etc.