Since atoms have more than one electron (other than atomic hydrogen) how do you account for the electrons remaining associated with each single atom rather than running away from one another leaving the nucleus without any electrons?

the electrons remain around the atomic nuclei due to the existence of a positive charge on the nuclei that, of course, atract the negative charged electrons. The protons are the paricles in the nuclei that hold the positive charge.

Justification:

First, I wish to explaing the sense of the question. The question arises because given that the electrons have negative electric charge how is that they do not repeal each other to the point that they end leaving the nucleous of the atom alone.

This is you know that equal charges repel each other, so how is it that the electrons stand around the nucleous instead of separateing and levaing the atomic nucleous alone.

The answer is due to the existence of a positive charge on the nuclei that, of course, atract the negative charged electrons. That positive charge is the protons.

The protons are particles in the atomic nuclei that are positive charged and they exert the right attractive force upon the electrons to permit them stay in the orbitals (regions of the space around the nuclei of the atoms where the electrons are found).