'expense on' is correct and usable in written English.
You can use it to refer to the amount of money spent on something, such as "The expense on groceries was more than expected this month."
He may write the legal bills off as an expensive but necessary expense on his road to redemption.
Languedoc-Roussillon spares no expense on this.
Many trainers spare no expense on their horses' good health.
Inside, Hervé has spared all expense on the décor.
Indeed, the publishers have spared no expense on the promo.
— Facebook will suddenly recognize a huge share-based compensation expense on its income statement.
It became nearly impossible to buy food except at great expense on the black market.
Mr. O'Leary traveled to the conference at his own expense, on Ryanair.
Neither does it show up as an expense on the income statement.
This requires effort and possible expense on the part of the individual.
Is it possible that multiculturalism stresses difference at the expense on integration?
