Privacy advocates got a big win last year, pushing through a landmark law in California. Now, before the law even goes into effect, they are moving to make the statute tougher.

Californians for Consumer Privacy, the nonprofit group behind the privacy law, announced a plan on Tuesday to give Californians new data rights and place new obligations on companies. Most significant, the proposal would require California to establish a data protection agency with the power to enforce the law and issue new regulations.

The group’s leader said he wants to amend the law through a ballot initiative next year. In order to do so, the group will need to first collect the valid signatures of more than 620,000 registered voters in California.

“People are waking up to the fact that they’ve lost control of their information and are trying to take that control back,” said Alastair Mactaggart, the founder and board chair of Californians for Consumer Privacy.