Some Republican House members, led by Freshman Maria Elvira Salazar, filed on February 8 a Dignity Act bill for immigration reform. The bill is summarized here and here. The bill highlight a labyrinthian process of normalization of unauthorized persons which includes levies on most, a kind of reparations, admitting to having committed a felony. Legalization can be held up if a political committee decides that more than 10% of persons crossing the Mexican border escape apprehension (apparently ignoring visa overstays).
Salazar was one of nine House Republicans who voted in March 2021 for the Democratic-created The American Dream and Promise Act. Democratic legislative proposals for immigration reform in 2021 included Biden’s Citizenship Act of 2021, the Farmworker Modernization Act, the Citizenship for Essential Workers Act, and the Dream Act of 2021 (go here for them all).
To add to the confusion, Salazar was a co-sponsor of a Republican reform bill in early 2021 which was also called the Dignity Act.
The last congressional reform bill which had bipartisan co-sponsorship was likely one introduced in 2018 (go here).
And, the 2020 Republican Party platform ignored any serious effort to normalize legal status and focused on the border wall and draconian measures.