There are variations that you will also hear
First, without 'Do' or 'Do you' or even the last 'you'
"You want me to go with you?" "Want me to go with you?" "Want me to go with?"
Second, 'come' instead of 'go',
"Want me to come with?"
Third, adding 'along' to 'with' or replacing it.
"Want me to come along?" "Want me to come along with you?"