Banks, gambling firms and online marketplaces such as Amazon and Temu are expected to be hit with higher taxes.
That would help to pay for support for poorer households facing high energy bills and to freeze fuel duty for drivers.
Healey says he wants to give Britain "a bit of breathing space" from the impact of the Iran war that is pushing up inflation.
"This budget is about getting through this difficult moment. But it's also about putting Britain on a future path, a better future path," he said in a statement.
His first budget - due to be announced in parliament on Wednesday - will detail how the government plans to give regional mayors more control over tax revenues, part of Burnham's devolution push.
Separately, more than Stg20 billion ($A38 billion) in extra support will go to state finance institutions to spur investment in artificial intelligence, defence and green energy by the early 2030s.
On entering Downing Street in July, Burnham promised "the biggest changes in the last 40 years", including a bigger role for the state in the economy.
But Healey's options are limited by the surge in borrowing costs for governments around the world including Britain, where investors remember the 2022 "mini-budget" of former prime minister Liz Truss and the ensuing bond market meltdown triggered by its unfunded tax cuts.
After big tax and spending increases in the two budgets of the previous finance minister Rachel Reeves, Wednesday is being framed as a "steady as she goes" moment for Britain's economy, which has so far withstood the Iran war energy price shock.
In an attempt to ease some of Reeves' big tax hit on employers, Healey has said he would reduce paperwork for businesses to save them Stg800 million a year.
Bigger policy changes - including how to fix the inflation hit to public spending - are likely to have to wait for a 10-year plan that Burnham has said he will announce later in 2026 and a broad spending review in 2027.
But Healey is under pressure to say now how he intends to pay more for defence - an issue that caused him to quit as defence minister in June in a move that hastened Keir Starmer's resignation as prime minister.
Healey's biggest hope is for an end to the Iran war, which would lower the government's bill for servicing Stg3 trillion of public debt.
