I think if the Republicans want to increase their base they should tone down and play up some things.
The Dems made a mistake losing sight of their traditional base - working people and instead focusing their attention on other groups and taking certain support for granted. I think that led to some big loses to Trump.
The Republicans have over the past few decades, made social conservatism a hot a major plank. More important than fiscal conservatism. I think that they should realize that certain things have sufficient majority popular support, they should marginalize the issues.
Marriage is one. The government recognizes marriages and the law provides certain benefits to married couples. The government is not going to stop doing that (I think that is more of a libertarian view maybe?) and America by far supports same sex marriage. So let it go. Why are you fighting it or making an issue of it? It has zero effect on anyone else's marriages. Another one is abortion which, is really a relatively recent issue. It did not spring straight fro RvWade - it was some time after that. It's another case where the American voters by far support legal abortion. Let it alone. Focus instead on the thornier issues surrounding it - when and how to allow late term? What about the ethics of abortion and fetal abnormalities? A third thing is immigration. Many people support the need for immigration reform and some sort of border control. But few supported the draconian and human-rights abuses of Trump era policies. I think that turned people away, particularly religious people.
If Republicans made immigration and "all Americans together" issue, instead singling out poor people, or Mexican people, for particular demonization, maybe they would get wider support from immigrant communities who are typically dominated by all business owners, entrepreneurs, and traditional cultural backgrounds. And if you had traditional conservative fiscal values, and support for traditional institutions like the military, police, and businesses - maybe the base would increase.
If they did, the Dems would be caught left footed. But then again - there is a lot they could do as well.
So maybe we just need more parties.