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Its Commons leader Ian Blackford asked for help to stop the "catastrophic damage" of "extreme" Brexit.
"It is time for MPs of all parties to put politics aside," he said.
Labour says the UK should "stay aligned" to the EU after Brexit and could pay to access the single market like Norway.
Mr Blackford said he would invite other opposition leaders to a summit on 8 January when MPs return from the Christmas recess.
He said: "As we saw with the successful amendments to the EU Withdrawal Bill, when opposition parties work together effectively it is possible to secure a parliamentary majority and deliver change in the national interest."
The SNP, Liberal Democrats, Plaid Cymru and the Greens have all said they want the UK to stay in the single market and customs union after Brexit - something Prime Minister Theresa May has already ruled out.
Labour's leader, Jeremy Corbyn, has also faced criticism over his refusal to support a second referendum on the final terms of the UK's exit from the EU.
He told the i newspaper: "We have had a referendum which came to a decision. The negotiations are still ongoing, albeit well behind schedule, and we've set out the kind of relationship we want to have with Europe in the future."
Tom Brake, Brexit spokesman for the Liberal Democrats, said the Labour leadership had "shirked their responsibility" to provide effective opposition to the government.
"The Labour leadership has constantly played a game of smoke and mirrors over their Brexit position.
"But here they are nailing their colours to the mast in support of hard Brexit," he added.