Welsh Labour is looking poised to go it alone and form a government without help from other parties.
Thursday's Senedd election left Labour with 30 seats - one short of an outright majority.
But a senior figure said the party could continue to run the Cardiff government without a deal signed with opposition politicians.
Labour minister Jeremy Miles said the result allowed them to work with parties on a "case-by-case basis".
Party leader Mark Drakeford also said Labour has governed successfully on 30 seats before.
With no significant challenge from the opposition to his position Mr Drakeford is expected to be reappointed to his job as first minister.
However, he may in future need help from the opposition to pass laws and get Labour's spending plans through the Welsh Parliament, with one seat short of a majority.
'No monopoly of good ideas'
Mr Drakeford told BBC Wales: "We have demonstrated over a number of governments that you can govern successfully on 30 seats, but I'm open to working with any party where there is common ground between us."
"I'm always much more interested in policy agreements that I am in a sort of political fixing."
He added: "No party has a monopoly of good ideas, and where there are things that we can work on together, then my administration will certainly look to do that with anybody who thinks that we can work to the advantage of Wales."
The Welsh government ruled in a minority from 2011 to 2016, striking deals with the Liberal Democrats and Plaid Cymru at various points to pass budgets.
Neath member of the Senedd (MS) Mr Miles said there were "precedents where we have successfully been able to negotiate budget agreements, legislative arrangements on a case-by-case basis with other parties".
"I think the mathematics of this Senedd, the response that the people of Wales have given, allows for that range of possibilities," he told the Sunday Supplement programme on BBC Radio Wales.
In the last Welsh government Liberal Democrat Kirsty Williams served as education minister.
Jane Dodds, the Welsh Lib Dem leader elected as their only MS this time, has ruled out joining the Welsh government.
She told the Dewi Llwyd ar Bore Sul programme on BBC Radio Cymru: "I'm not expecting [an invite to join the government] and I don't want it to tell you the truth."
"I don't have the experience of being in the Senedd. Kirsty had 15 or 16 years in the Senedd before she had a chance to be in the cabinet."
Mark Drakeford is in no rush. Having led Labour to a record-equalling tally of seats, he is not under pressure within the party.
But tough times lie ahead. The pandemic is not over. The outlook is uncertain.
In those circumstances, haggling over votes, lurching from deal to deal, is not an appealing prospect.
That's why Mr Drakeford is sounding conciliatory.
He wants stability in the Senedd and, if there is not to be a formal coalition, he must co-operate with opponents.
Welsh Conservative Senedd leader Andrew RT Davies saw the party's seats increase from 11 to 16 - the Tories' best-ever result, although far short of the numbers needed to govern.
Mr Davies said: "We've got the best result we've ever had in the assembly, nearly 50% more members returning, a new generation of Conservatives, the first lady coming to the assembly from an ethnic minority as well."
He told BBC Radio Wales he would like the next term's presiding officer (PO) - who chairs meetings and is a figurehead for the Welsh Parliament - to be from his party.
"I think it is important to reflect on the success of the Conservatives in this election, and give consideration to maybe a Conservative PO or DPO (deputy presiding officer)," he said.
"I do think that from a consensual point of view, I think a progressive move would be to offer that consideration around a Conservative appointment."
Plaid Cymru came third at the election. Although its overall seat tally rose by two, it lost its prized constituency seat of the Rhondda in the south Wales valleys.
The party's leader Adam Price told BBC Radio Wales' Sunday Supplement it was a "disappointing result" for Plaid Cymru electorally and a "bitter blow" in the Rhondda.
But he said there were "many positives".
He said Plaid Cymru had "opened up the space for the Labour Party, and Mark Drakeford himself, probably, to take up a much more radical line on the constitution".
"This is an election which actually has strengthened belief in Welsh self-government and in Welsh democracy," he added.
Last night Prime Minister Boris Johnson invited the first ministers of Scotland and Wales to a summit on how "Team UK" can recover from the pandemic and face other "shared challenges".
Welsh Labour Housing minister Julie James said she welcomed the invitation to a meeting if it was "real".
She told the BBC's Politics Wales programme: "We've been calling for many many years for a proper constitutional summit, where we talk properly about the role of devolution across the UK."