It looks like the beginning of a united plan for the Senate impeachment trial is in the works. According to a New York Post article the House impeachment managers would present their prosecution case; then President Trump’s designated lawyers will present his defense case; then the Senate will vote.
At least, that’s the plan being reported:

WASHINGTON – After weeks of behind-the-scenes debate, Senate Republicans have hit on their strategy for handling President Trump’s impeachment: a brief trial — with no witness testimony — and a fast acquittal.
“I’m ready to vote now,” Sen. Josh Hawley (R-Missouri) told The Hill. “I think the articles are a joke.”
But they don’t want to dismiss the House Democrats’ charges out of hand, as some Trump allies have proposed.

“It’s time for him to have his day in court,” Hawley said. “The president deserves to have due process.”
Trump, who was calling for a full-blown trial with multiple witnesses — including former Vice President Joe Biden and his son Hunter — just three weeks ago, now supports the Senate leadership’s plan. (read more)