A powerful new bloc in the Senate is forming — one that has the potential to be a make-or-break force for government legislation.

Key points: David Leyonhjelm, Fraser Anning and Cory Bernardi hope One Nation's Brian Burston will join their group

David Leyonhjelm, Fraser Anning and Cory Bernardi hope One Nation's Brian Burston will join their group They get briefed by Government together, discuss legislation together and negotiate

They get briefed by Government together, discuss legislation together and negotiate Senator Burston has had a public falling out with his party leader, Pauline Hanson

In the ruins of One Nation's latest falling out, four conservative senators from four different parties are set to band together.

The group already includes Liberal Democrat David Leyonhjelm, Katter's Australian Party senator Fraser Anning and Australian Conservatives senator Cory Bernardi.

And Senator Leyonhjelm told the ABC he was confident former Pauline Hanson loyalist Brian Burston would also join the loose alliance.

"Oh yes, I think so," Senator Leyonhjelm said.

"I know Brian very well. He and I have been quite friendly in the whole time he's been in the Parliament. I think he'd be pretty interested."

Senator Burston and his One Nation leader had a spectacularly public falling out last week when he announced he would cross the floor and support the Coalition's company tax cuts.

It is difficult to see how Senator Burston can remain in One Nation, especially because his leader has demanded his resignation.

Sorry, this video has expired Pauline Hanson fights tears on national TV, claims Brian Burston has tried to defect

But Senator Leyonhjelm said his crossbench colleague would not have to travel solo, inviting him to join the "little alliance".

"We meet together as a group and decide our position," Senator Leyonhjelm said.

"We get briefed by the Government as well together so that we can all ask our own questions.

"Once we've sorted out our position, then we negotiate with the Government as a group as well."

While they are not committing to always voting the same way, the senators argue their alliance gives them more power and more negotiating heft.

Senators Bernadi and Leyonhjelm accompany Senator Fraser Anning into the Senate. ( ABC News: Jed Cooper )

They would also form a powerful potential bloc in the Upper House.

Less than two years ago, One Nation and the Nick Xenophon Team were the most influential on the crossbench, but infighting has diminished their size and power.

Senator Bernardi argued there was stability for Senator Burston post One Nation if he decided to leave or was expelled from the party.

"He will be strengthened by cooperating with us and we will be strengthened by having his input as well," Senator Bernardi said.

One Nation leader Pauline Hanson has asked senator Brian Burston to leave the party. ( AAP: Mick Tsikas )

Assuming the loose alliance sticks, the Coalition could lock in half of the crossbenchers it needs — if Labor and the Greens do not support its bills.

"It gives us the ability to shape legislative outcomes and it's easier for the Government, quite frankly, to deal with a group of people who are trying to pull in the same direction," Senator Bernardi said.

In a game of herding cats, a new bloc of four would at least allow the Government to sharpen its negotiating strategy.

Senator Leyonhjelm argued working together was usually better than acting alone.

"Sometimes that works, sometimes it doesn't work," he said.

"But the idea is that if we do all agree and the Government needs our votes and we're minded to withhold our votes because we don't feel particularly strongly about the legislation, then we might extract more concessions from the Government than we otherwise would."

It is still unclear where Senator Burston will find a political home, if he is sacked from One Nation.

And even in this group, there is no guarantee of stability. After all, it brings a libertarian under the same roof as social conservatives and protectionists.

But the senators insist much more unites them than divides.