Not many homes in Los Alamos have basements; probably because of the lack of soil - usually run into rock after about 2 feet down. There are quite a few walkouts along the canyons on Barranca Mesa and North Mesa. Most "large family" homes are either custom built or converted and remodelled older duplexes or quadraplexes. I have a whole duplex on the market with 8 bedrooms and 2 baths but has never been turned into one living unit.
Depending on your price range, there are some choices for a large family. I sold one in White Rock a couple months ago that had five bedrooms and a basement. Some of the condo units even have 3 bedrooms, large loft and full walkout basement (some of which have been turned into multiple bedrooms, offices, play spaces etc.