The ruling Palang Pracharath Party (PPRP) says its charter amendment bill will leave the Senate's role in choosing a prime minister untouched.
Chief government whip and PPRP list MP Wirach Ratanasate said on Friday MPs and senators had agreed to hold a joint parliamentary session on June 22-23 to discuss charter proposals.
A charter amendment bill put forward by PPRP deputy leader and list MP Paiboon Nititawan has already been submitted to parliament.
Other parties are expected to table separate proposals to parliament next week and all will then be considered by parliament.
Mr Wirach said the bill proposed by Mr Paiboon included charter provisions associated with the voting system, seeking to revert from a single ballot for constituency and party-list MPs to two separate ballots.
Critics say the single-ballot system has made it difficult for political parties to grab a parliamentary majority and form a single-party government.
However, the bill leaves untouched Section 272 of the constitution which allows the Senate to join MPs in the selection of the premier.
The section has been widely criticised as being a tool to keep Prime Minister Prayut Chan-o-cha in power.
Mr Wirach said other government coalition parties might have their own charter amendment proposals but lack enough support to table these in parliament.
In light of this, the PPRP was ready to support their motions, even though these must share similar principles, particularly the key proposal to leave the Senate's power in choosing the prime minister intact, Mr Wirach admitted.
Under the constitution, a charter amendment motion needs the signatures of at least one-fifth of the House to be tabled in parliament.
Cholnan Srikaew, an MP for the main opposition Pheu Thai Party, said it would submit five charter amendment bills -- all had been signed by its MPs and were ready to be tabled.
One seeks to revise Section 256 of the charter to pave the way for a charter drafting assembly; one to push for further rights and liberties; and one to deal with the voting system.
Another bill targets Section 272 and another seeks to abolish charter provisions legalising all announcements and orders of the now-defunct National Council for Peace and Order, Mr Cholnan said.
Pheu Thai secretary-general Prasert Chanthararuangthong said opposition parties would submit their charter amendment motions to parliament next Tuesday or Wednesday.
They would first meet on Monday to thrash out their differences before submitting the bills to parliament, Mr Prasert said, adding that about 100 Pheu Thai Party MPs had signed in support of its proposals.
"For the sake of unity, we will have to listen to opinions from other opposition parties since we have been working together a long time," he said.