Monday's vote would allow dispensaries to grow and sell more than three varieties of pot to patients and to provide the drug in an edible form to children.
The measure was inspired by families who said their children with severe epilepsy would benefit from using certain types of marijuana.
Lawmakers passed a bill in June, but Gov. Chris Christie last month issued a conditional veto. He said he will approve the bill if it does not eliminate the requirement that at least two doctors sign off before children can have access to medical cannabis.
The state Senate has already accepted Christie's revisions.