None of the four alternatives to British Prime Minister Theresa May's Brexit deal receives support from a majority of MPs in the second round of "indicative vote", which kicked off at around 20:00 BST on Monday and whose results were announced at around 22:00 BST.
After the latest round of indicative votes failed to produce a clear victor, Brexit Secretary Stephen Barclay said: "If the House were to agree a deal this week it may still be possible to avoid holding European parliamentary elections".
The second referendum proposal garnered the most votes in favour - 280 - but was beaten by 292 votes against.
Mr Clarke's customs union option lost by 273 to 276, just three, while the common market 2.0 option lost by 261 to 282.
Mr Barclay said that if the House of Commons is able to agree a deal this week, it would still be possible to avoid European Parliament elections in May.
Attorney General Geoffrey Cox speaks in the House of Commons ahead of the Brexit debate
"It has once again failed to find a clear majority for any of the options", he said.
Chief executive of London First, Jasmine Whitbread, said: "Once again, Parliament has failed to back a horse and, once again, we find ourselves with only days to go before we are due to leave the European Union without a deal - the one thing Parliament does agree we should avoid".
Theresa May's Conservative Party isn't actively preparing for a general election (GE), its deputy chairman said, even as Parliament looks set to push her to adopt a proposal for a softer Brexit today, three days after resoundingly rejecting her plan for a third time.
Amidst the debate, Conservative whip Nick Boles resigned from the role, saying he had tried to find a "compromise" for Brexit but said he had "failed".
"The Conservative Party has shown itself to be incapable of compromise", he said. "I regret therefore to announce I can no longer sit for this party", he said.
"Therefore the only option is to find a way through which allows the United Kingdom to leave with a deal".
"The government continues to believe that the best course of action is to do so as soon as possible".
Brexit Secretary Stephen Barclay told MPs that if they wanted to secure a further delay from the European Union, the Government must be able to put forward a "credible proposition" as to what it would do.
The EU has called an emergency summit for April 10 and warned that without a plan, Britain risks abruptly ending ties with its largest trading partner two days later, causing huge economic disruption.
Voting took place from 8pm and the first result came in shortly after 10pm tonight.
MPs voted down all the four Brexit proposals chosen by House Speaker John Bercow in a bid to break the current Brexit deadlock.
The votes by MPs are not legally binding but carry political weight, and the government fears they may lead to legislation that would force May's hand.
Labour leader Jeremy Corbyn described the continued deadlock as "disappointing", but said MPs should have another chance to consider the alternatives on Wednesday.
"A hard Brexit becomes almost inevitable", warned Guy Verhofstadt, who chairs the European Parliament's Brexit Steering group, after the votes.