Campaigners on both sides lobbied MPs before May's vote
A cross-party group of MPs will attempt next week to end the requirement for a second doctor to give their approval for an abortion to take place.
They have also put forward proposals to scrap the need for some abortion drugs to be taken on approved premises.
But when the Human Fertilisation and Embryology Bill returns to the Commons on Monday there will also be a fresh attempt to cut the 24 week upper limit.
In May MPs rejected cutting the 24 week limit in a series of votes.
A series of amendments have been put forward to the bill - although it will be up to Commons Speaker Michael Martin whether or not they are debated and voted on.
Labour's former health secretary Frank Dobson, Tory frontbencher Jacqui Lait and Liberal Democrat frontbencher Evan Harris are backing proposals that would ease aspects of abortion law.
These include reducing the number of doctors required for approval from two to one and scrap the need for some abortion drugs to be taken on approved premises.
It would also allow nurses with relevant qualifications to carry out early stage abortions and increasing the number of places where they could be carried out.
If supported by MPs, they would be the first changes to the 1967 Abortion Act since 1990, when the upper limit for terminations was reduced from 28 to 24 weeks.
The amendments reflect the findings of the Commons science and technology committee's report last October, which suggested that requiring women seeking abortion to get approval from two doctors might be causing delays.
It also called for more nurses' involvement in early abortions.
But not all members of the committee agreed with the report - Conservative MP Nadine Dorries and Bob Spink, a former Tory who has since joined the UK Independence Party published their own report, saying MPs had been "misled" on some issues.
Debating the Bill in May, MPs rejected a series of options to reduce the upper time limit for abortions - the closest vote was an attempt to bring it down to 22 weeks, which was rejected by 304 votes to 233.
Prime Minister Gordon Brown and most of the cabinet voted to keep the existing 24 limit, as did Liberal Democrat leader Nick Clegg.
Conservative leader David Cameron voted for a 20 week limit and then for a cut to a 22 week limit - which was backed by most of the shadow cabinet.
Ms Dorries, who led the campaign to reduce the limit, has tabled her own amendment to the bill, which returns to the Commons next Monday - again asking for the limit to be reduced from 24 to 20 weeks.