People are being asked to share their view on plans to expand the Welsh Assembly by an extra 20 to 30 members.
An expert panel said the move was necessary to cope with the growing workload as more power is devolved.
Also, the vote would be given to 16 and 17-year-olds as part of proposals to reform the 60-member assembly.
Presiding Officer Elin Jones hailed “the opportunity to forge the national parliament that the people of Wales deserve to champion their interests”.
The assembly is already due to be renamed the Welsh Parliament as a result of a previous consultation.
Powers for the assembly to change its electoral rules, size and other internal affairs are being granted under the 2017 Wales Act.
Last week, AMs voted in favour of putting the expert panel’s recommendations out to public consultation.
Ms Jones said: “The Wales Act 2017 marks the start of a new phase of devolution in Wales, giving us the opportunity to make profound changes to our legislature.
“We now have the opportunity to forge the national parliament that the people of Wales deserve to champion their interests.”
The panel, chaired by Prof Laura McAllister of Cardiff University, also recommended a change in the voting system, to a proportional method called the Single Transferable Vote.
One option would be to pair the current 40 constituencies to merge them into 20 seats, each with four AMs, giving a total of 80.
A gender quota would boost the number of women in the Senedd, and the option of standing as a “job share” candidate would aim to encourage people with disabilities or caring responsibilities.
Any changes will require a law to be passed in the assembly with a two-thirds majority.
When the report was published in December, Welsh Labour said it would not give its view until its 2019 conference, which Plaid Cymru AM Simon Thomas said “kills dead” any chance of reform before the next election in 2021.
The consultation is open until 6 April.
In January, the Welsh Government proposed votes for 16 and 17-year-olds in council elections as part of a package of local government reforms.