The Greens are trying to get the threshold for entering Parliament lowered to 4 percent.
MP Golriz Ghahraman's Electoral Strengthening Democracy Bill would lower it from the current 5 percent, as recommended by an Electoral Commission review of the MMP system conducted in 2012.
It would also remove the coat-tail rule, which lets parties that win an electorate bring in more MPs according to their share of the party vote, even if they didn't reach the threshold.
"New Zealand proudly has a strong democratic system, our MMP system is rightly representative," said Ms Ghahraman, who scraped in on the Green Party list after the special votes gave her party an extra seat. She was ranked eighth.
"In saying this, there is definitely room for improvement to ensure we have the best democratic system possible and that access is fair."
Other changes the Bill would make include giving prisoners the right to vote, enable Māori voters to switch rolls whenever they want and ban political donations from offshore.
"The Bill seeks to stop unfair influence and potential corruption in politics," said Ms Ghahraman.
"We should absolutely not be seeing political donations come from overseas and we need to reduce the anonymity threshold so that we can see who is donating to political parties."
The Greens got 5.9 percent at the last election, plummeting in the polls ahead of the election after then co-leader Metiria Turei admitted historic benefit fraud.
The only party in recent years that has failed to reach Parliament after polling between 4 and 5 percent is New Zealand First. In 2008 Winston Peters' party failed to get into Parliament after getting 4.07 percent and no electorate seats.
In 1999 NZ First got 4.26 percent but won five seats, thanks to Mr Peters' success in Tauranga.