The House of Representatives will vote Wednesday on a resolution to open an official impeachment inquiry into President Biden for his alleged involvement with his son’s and brother’s overseas business dealings — involvement that Democrats and some Republicans are saying has yet to be proven. 

The purpose of officially authorizing the impeachment inquiry is to give the House more legal heft when forcing testimony from witnesses, though some GOP moderates have so far declined to endorse the resolution. 

“We are formalizing … impeachment inquiry efforts to give the House the strongest legal standing to pursue needed information and enforce subpoenas,” the chairman of the Rules Committee, Congressman Tom Cole, said on Tuesday. “Allowing this chamber to be at the apex of its constitutional power is vital to our system of checks and balances.” 

Late Tuesday, the committee sent the impeachment inquiry authorization resolution to the floor, with all nine GOP committee members voting yes and the four Democrats voting no. The full House will vote Wednesday. 

Authorizing an official inquiry has become a key priority for the House GOP in recent weeks after the younger Mr. Biden refused to comply with a subpoena from the Oversight Committee that requires him to appear for a closed-door deposition. Mr. Biden has instead said he will only testify publicly before the committee, which Republicans say violates the subpoena. They are threatening to hold him in contempt of Congress if he fails to appear for a deposition Wednesday morning, which could lead to more federal charges for the first son.

“It is a deeply sad day and is an occasion I do not relish,” Mr. Cole said in his opening statement. “Nor, I am sure, do any of my colleagues in the room. Nonetheless, this is a weighty responsibility, one that we all take very seriously, and we must do our duty for ourselves, for the institution, and for the nation.”

He made sure to point out that a vote to open an official impeachment inquiry is not a vote to actually impeach the president — a justification that some of the more moderate members of the House have adopted.

“We are here to determine a process — not an outcome,” Mr. Cole said. “We are here to assert our Article I responsibilities — not to act as judge or jury. And we are here, fundamentally, to chart a path forward that unveils facts to the public.”

Several House Republican moderates who sit in districts won by the president in 2020 agree with Mr. Cole — that impeachment itself is not inevitable if the inquiry is opened.

A Biden-district member, Congressman Don Bacon, said Tuesday that he will vote to authorize an inquiry even though he sees no evidence that merits impeachment. A more moderate member from South Dakota who serves as the chairman of the centrist Main Street Partnership, Congressman Dusty Johnson, said the same. 

One member who flipped a seat from blue to red last year and is now a top 2024 target for Democrats, Congresswoman Jen Kiggans, told CNN that “the American people deserve to know answers to questions, however, I really also believe that we need to continue to focus on the priorities that we had coming into this Congress.”

The Rules Committee’s top Democrat, Congressman Jim McGovern, said Republicans are simply doing President Trump’s bidding in moving forward with impeachment. 

“This impeachment sham is — to put it bluntly — an extreme political stunt,” he said. “Let me tell Republicans right now: you will fail because the simple truth is your so-called investigation is built on a lie. Republicans began this ludicrous exercise the second they took control of this House of Representatives.”

The defense of the first son has relied in part on his history of drug and alcohol addiction. Democrats say the younger Mr. Biden was simply too damaged following the death of his brother and turned to a life of drugs, which led him to make financial mistakes, like avoiding paying personal income tax. 

“This is someone with a lot of trauma in his life and who sadly turned to drugs,” Mr. McGovern said of Mr. Biden. “We’ve seen that Republicans have sought to weaponize that trauma and use it to attack President Biden and his family. Frankly, it’s just disgusting. I mean, we literally had Marjorie Taylor Greene hold up explicit photos of Hunter Biden at a committee hearing.”

Republicans weren’t buying that, however. “Everybody has problems, and a lot of people go through the same things, but everybody in America has to pay tax, everybody has to account for money they make, everybody should not get the [plea] deal Hunter Biden was trying to get,” a conservative member of the committee, Congressman Ralph Norman, said to the committee Democrats. 

“We’re not here to litigate the merits of impeachment but simply to proceed with the process of an impeachment inquiry for this body — the House of Representatives — to be able to conduct its oversight function,” Mr. Roy said. “We have seen an extraordinary amount of stonewalling from this administration.”

Mr. Roy pointed to two Department of Justice tax prosecutors who claim to have evidence that they were obstructed when trying to investigate Mr. Biden. The prosecutors, Mark Daly and Jack Morgan, have been subpoenaed by the Judiciary Committee but have been blocked from testifying by the Biden administration.