I don't own a STR yet, but my husband and I have 5 kids and love to travel. Consequently we've stayed in a lot of STRs. We don't always get charged extra, but we often do. I generally expect to be charged extra for each person after the first 2, and am pleasantly surprised when they don't.
As far as sleeping arrangements go, Lots of places have a futon in the livingroom or a couch that turns into a bed so they can sleep 2 more people. In fact, we've had that more often than not.
Personally, it doesn't bother me if my kids sleep on a futon or sofa bed, but if I had to pay extra for 7 people and then they gave us air mattresses I'd be a little annoyed.
I think the best use of space I've seen was a 1bdrm 1 bath we stayed in for a week an hour or so north of Seattle. The listing was on VRBO. They had 2 futons in the livingroom that folded out into beds, then they had built a kind of "L" shaped wall out of recycled doors (it actually looked pretty cool) and put a bunk bed that was a full on bottom and a twin on top on the other side of it. Then there was the actual bedroom with a queen bed in it. Technically that place could have slept 9 - 9 might have felt a tad crowded, but we were very comfortable for a week with 7 people.