One vote will focus on US aid for Ukraine, which has stalled in recent months after Congress refused to renew Mr Biden’s mandate to send American munitions to Kyiv.
A second will deal with support for Israel, which had been attached to the Ukraine funding in the White House’s own supplemental package.
Congress is under increasing pressure to continue its support for Israel since Iran launched an unprecedented attack on military targets there on Saturday.
A third vote could authorise support for Taiwan, where the Biden administration has said it is concerned about Chinese military buildup, and other allies.
A fourth will address other measures that are popular with Republicans and had been mooted as a way to sweeten the package for its critics.
Speaking after the meeting, Mr Johnson said the “overall concept” of his plan was the same as Mr Biden’s package.
“It’s the same places that the funding would be sent, and you’ll see the House’s take on it,” he said.
The plan could resolve a congressional holdup in foreign military aid that began in October, when Mr Biden’s first supplemental plan was rejected.
The US president requires the continued support of Congress to send Ukraine and other countries weapons from American military stockpiles.
However, some Republicans have signalled they will not vote for a compromise package between the GOP-controlled House and the White House.
Mr Johnson is already facing a rebellion from some Republican representatives, led by the hardline conservative Marjorie Taylor Greene. Some have called for him to be ousted from the Speaker’s chair, just months after Kevin McCarthy was removed by a similar rebellion in October.
Mr Biden and his officials have warned that without further aid, Ukraine will lose its war against Russia.
