Building a basement without basement tool on preexisting home

The only thing I can think of would not work on a existing building. But you could use the terrain tool to either lower or raise the terrain, do it to the same height as a wall (place one section of a wall outside of the area you are changing the terrain height - to use as your guide for height) and then also lower/raise the terrain for the size you want the basement. I think you would have to make it a walk-out basement because it will technically be your first floor without the use of the basement tool. (I am not sure if your second floor with a door would count as the main front door sims auto go to or not - you will have to test that out - unless someone on the forum knows and replies also)

I have also found some really good videos about building info, tips, etc. by just googling what I am trying to build. You should check it out - there are some really talented simmers with amazing builds.  (be sure to include sims 3 in your search title otherwise you will get information pertaining to the other sims games

Wish I could help you more

Before the patch and pack came along basements where built using the foundation tool search carlsims3guide they may have a tutorial up 

Do however before you start building a basement save your game then save as new name if it messes up then you will still have your original save safe and untouched