# Why can't we decompose the position wavefunction differently?

If I understand correctly, we see the electron appear as a point on the detector in the double slit experiment because the position basis vectors are orthogonal. This ensures that we will only see one of these possible outcomes due to decoherence. However, isn't it possible to decompose the wavefunction of position differently? Why can't we make the basis vectors some combination of locations so that we observe some combination of points appearing on the detector?