Building permit after preliminary building approval

The municipality needs this anyway. The preliminary decision only "checks" whether the planning complies with public-law requirements. The points listed in the preliminary decision are therefore not checked again. However, the application with all other points undergoes the normal procedure.

The application for early commencement of construction can be approved without further examination and allows you to begin the construction work specified therein before the actual building permit. However, the submitted application must comply with building and planning law. Since you have already received the preliminary decision, it can be assumed that everything is approvable and that rejection of the application and the associated dismantling are not to be expected.

Which other things need to be checked?

... I guess that's similar to what Musk did with the Tesla factory, right?

Maybe you should show the plans (as they are, and additionally marked with the changes you want). Do you have any reason to assume that there is still room in the existing plans, i.e. that the floor area ratio and a possible partial storey of the attic have not been fully utilized?