Representative Houston Gaines added a provision against allowing local governments and hospitals to take homeless people to other counties without permission.
The House voted 99 to 76 to pass Senate Bill 62 on Monday, because the House Committee amended the measure to add the ban on dumping.
It goes back to the Senate for more debate.
Democrats accused Republicans of trying to criminalize homelessness and impose unworkable requirements on local governments.
The bill would allow transport if and accepting facility agreed.