An investigation has found that four members of the Welsh Parliament drank alcohol on its premises, days after a Wales-wide alcohol ban came into force.
The Senedd has referred the "possible breach" of Covid rules to Cardiff Council and its own standards watchdog.
Conservative group leader Paul Davies has apologised and won the "unanimous" support of the group to stay in post.
Mr Davies, Tory chief whip Darren Millar and Labour's Alun Davies deny breaking any rules.
Alun Davies has been suspended from the Labour group in the Senedd.
BBC Wales has asked for clarification as to the identity of the fourth Senedd member investigators have referred to.
On 8 December, five individuals - four members of the Senedd (MS) and the Conservative group's chief of staff Paul Smith - were found to be consuming alcohol in the Senedd's licensed tearoom, according to an investigation by the Senedd Commission.
Four days earlier a ban on the serving of alcohol in pubs and licensed premises across Wales had been imposed, leading the investigation to conclude the incident could amount to "a possible breach" of Covid-19 regulations.
The Senedd's Presiding Officer Elin Jones MS said the matter had been referred to Cardiff Council to investigate a possible licence breach.
"The regulations in place at the time imposed strict restrictions on members of the public with regard to the consumption of alcohol," she said.
"Given that the possible breach in question occurred as a result of the consumption of alcohol by Members of the Senedd, I have also written to the Standards Commissioner to ask him to investigate whether these Members acted in accordance with the duty in the Code of Conduct to conduct themselves in a manner which maintains and strengthens the public's trust and confidence in the integrity of the Senedd."
In a meeting earlier, the Conservative group in the Senedd met to discuss what a statement issued on behalf of group chair Janet Finch-Saunders MS detailed as "events involving three members of the Group" on 8 December.
"The Group extended its unanimous support for Paul Davies to continue in his post as Leader of the Group," the statement read.
BBC Wales has been told by several sources that Mr Davies said in the meeting he had considered resigning as leader.
It is also understood the declaration of support was made before Tory group members had seen the Senedd investigation's conclusion.
A grassroots Conservative Party member said it "won't hold with the party membership" if Mr Davies did not resign.
"The grassroots are on fire at the moment. He 100% needs to go now - his position is untenable," the member added.
When asked his opinion at the latest Covid press conference, First Minister Mark Drakeford said he hoped the sole member of tearoom staff on duty that evening would not be blamed for the incident.
"I'm very anxious that this does not all result in that person carrying the can for what happened that evening," he said.
"That was a single female member of staff faced with a collection of senior Senedd members.
"The idea that the person, the staff member, was to blame seems to me completely incredulous and I very much hope that this does not head in that direction."
'Should set an example'
Plaid Cymru MS Helen Mary Jones said: "Failure to address the members' actions is a grave error of judgment on behalf of the Conservative Senedd group.
"Their leader and their chief whip [Mr Millar] should be setting an example in the middle of a pandemic rather than getting embroiled in an incident which is in danger of bringing the Senedd into disrepute.
"It would seem that the internal machinations of the Tory group is stopping them from doing the right thing," she added.
Cardiff Council confirmed the city licensing authority - a Shared Regulatory Service (SRS) also covering the Vale of Glamorgan - had been asked to investigate.
"The service works closely with South Wales Police to ensure that public protection and adherence to Covid regulations is maintained," a spokesperson said.
"Once the investigation is concluded, and if a breach of the regulations has been found, SRS will take the necessary action, which could see a fixed penalty notice served or a prosecution in the courts."