Two U.S. senators have again introduced legislation that aims to protect Americans’ personal data, adding to Washington’s efforts to act on the issue.

Sen. Amy Klobuchar, the Minnesota Democrat and possible presidential candidate, and Sen. John Kennedy, the Louisiana Republican, on Thursday rolled out their Social Media Privacy and Consumer Rights Act. In the prior Congress, Klobuchar and Kennedy also teamed up to push privacy legislation.

“Our legislation would ensure that companies use plain language to explain to consumers how their data is being used, allow consumers to opt out of certain data tracking and collection, and require companies to notify consumers of privacy violations within 72 hours of a breach,” Klobuchar said in a statement.

The bill also would require that online platforms have a privacy program in place, and it aims to improve the remedies that are available to users when a data breach occurs.

Kennedy said: “I don’t want to regulate Facebook or any private social media company, but these platforms continue to compromise their users’ private data.”

The bipartisan legislation comes after Florida Republican Sen. Marco Rubio introduced his own privacy bill on Wednesday, saying it should prevent outrages along the lines of Facebook’s Cambridge Analytica scandal. Rubio’s American Data Dissemination Act would require the Federal Trade Commission to submit detailed recommendations for privacy requirements that Congress could impose on tech companies, and then if Congress failed to act within two years, his bill would enable the FTC to put into effect its own rules. Tech giants are, in large part, seeking federal regulation that could preempt California’s own tougher new rules.

Lawmakers and watchdog groups are increasingly scrutinizing Facebook Inc. FB, +2.66% , Alphabet Inc.’s GOOG, +2.39% GOOGL, +2.07% Google and other tech heavyweights over how they handle their users’ data, as well as how they deal with misinformation and political bias, with the attention coming thanks to recent scandals and Silicon Valley’s growing power. Privacy-related actions such as new federal standards are rated as “possible” by lobbyists at Hogan Lovells, in their recent report on what the 116th Congress is likely to deliver.

Separately, U.S. regulators have met to discuss imposing a record-setting fine against Facebook for an agreement to protect the privacy of its users’ personal data, said a Washington Post report on Friday citing unnamed sources. The fine under consideration at the FTC would represent the first major punishment levied against Facebook by the U.S. government since the Cambridge Analytica news broke in March.