Republicans would need control of at least 34 state legislatures to be able to call such a convention, and 37 to ratify any amendments.
So far they have unified control of 31 state legislatures. Of those 31, 19 have signed onto an application for an Article V Convention put forward by Convention of States, a conservative activist group.
https://www.businessinsider.com/constitutional-convention-conservative-scholar-states-2022-8
https://www.businessinsider.com/constitutional-convention-conservatives-republicans-constitution-supreme-court-2022-7
Something that I think about once in a while is that conservatives love capitalism and they praise the benefits of industrialization, but they also love localism, resent "multiculturalism" and put a lot of emphasis on the distinctions between the 50 states. And they don't seem to realize that capital accumulation (and the related development of more and more complicated global supply chains & information/media systems) is exactly what has diminished the importance of local cultural differences.
They get angry when liberals & leftists say things like "the states aren't really that essentially different from each other when it comes to how you experience life", or "state distinctions don't matter anymore" or "all suburbs are kinda the same", but I think that conservatives know deep down that the liberals & leftists are kinda right about this.