The federal government says it’s willing to negotiate further changes to the remainder of its planned changes to family tax benefits.

The Senate on Monday night passed a bill to scrap family tax benefit part B for couples whose youngest child has turned 13, with Labor’s support.

Social Services Minister Christian Porter told ABC radio he is now seeking the support of the crossbench to help pass $4 billion of other savings, which he will re-introduce to parliament on Wednesday.

Among the proposals is to exempt grandparent and great-grandparent carers, as well as single parents over 60, from changes to FTB part B.

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“I’d rather have a save compromised but actually have a prospect of passing through parliament, which means we actually get reforms to child care, than be doctrinaire about it all and be unwilling to compromise, so compromise it is,” he said on Tuesday.

A crossbench senator who supported rolling back benefits says that in a “perverse way” he is pleased it didn’t go as far as the government hoped.

Liberal Democrat David Leyonhjelm supports the principle of the changes but is worried the government was going to misuse the savings on additional support for child care.

“The savings yesterday were probably enough to buy all the kids an extra box of crayons,” he told reporters.

“I think that is probably a box of crayons more than they require.”

Child care was “excessively subsidised”, Senator Leyonhjelm said. “We’ve got more useful things to do with the money, including lowering taxes.”