The Pheu Thai Party is struggling to secure enough support from other parties for its prime ministerial candidate Srettha Thavisin.
It is now trying to woo support from the United Thai Nation Party (UTN), while the Move Forward Party (MFP) has apparently snubbed it.
The Palang Pracharath Party (PPRP), meanwhile, has expressed a willingness to back Pheu Thai's PM candidate.
Somsak Thepsutin, a Pheu Thai list-MP, said he met Thanakorn Wangboonkongchana, a UTN list-MP, for talks on the possibility of the UTN joining the Pheu Thai-led coalition.
Mr Somsak said he disagreed with the idea of some of the UTN MPs acting as renegades and breaking away from the UTN to join the coalition. "The whole party should come and join together," he said.
He refused to comment when asked if the Pheu Thai-led coalition needs to include the UTN and the PPRP.
However, he added: "Everything is possible. The new government wants to secure enough support to ensure stability."
The PPRP MP for Kamphaeng Phet, Phai Lik, who spoke on behalf of his party, said it had not been approached by Pheu Thai since they last met for talks on July 23.
However, the PPRP agreed that the new government must be established as quickly as possible so it can address the problems besetting the country.
"Therefore, the party agrees that all of its 40 MPs will vote for a prime ministerial candidate from Pheu Thai," he said.
"During talks with Pheu Thai [on July 23], we discussed the policies we want to push for together, such as increasing monthly allowances for the elderly and the continuation of the state-welfare card scheme.
"Moreover, several [PPRP] MPs used to work with Pheu Thai. I am also a former Pheu Thai MP," Mr Phai said.
He went on to say the PPRP has not yet discussed with Pheu Thai the possibility of joining a new government.
"But if Pheu Thai approaches us, we are ready to join," Mr Phai said.
Pheu Thai on Thursday welcomed the Chatthaipattana Party, along with its 10 MPs, into its bloc, raising the number of House seats held by the coalition to 238 out of the 500 total.
Both parties expressed their commitment to seeking cooperation from all political parties and the Senate for the election of a prime minister and the formation of a new government.
Pheu Thai leader Cholnan Srikaew said the country is in a unique political situation, and all parties needed to join forces to address constitutional issues, economic challenges and social conflicts.
The two parties urged the public to have confidence in their alliance, which they said is intended to bring Thai society back to normal quickly.
Chartthaipattana leader Varawut Silpa-archa said he thanked Pheu Thai for inviting his party into the coalition.
He cited their shared policies and perspectives and expressed confidence in Pheu Thai's potential to lead the upcoming administration.
With the inclusion of Chartthaipattana, the Pheu Thai-led coalition alliance now consists of nine parties.
Earlier, Pheu Thai withdrew from the previous eight-party coalition led by the MFP.
Pheu Thai, which has 141 House seats, on Monday, teamed up with the Bhumjaithai Party with 71 seats. On Wednesday, it announced its coalition had six more parties.
Deputy Pheu Thai leader Phum- tham Wechayachai said a meeting between Pheu Thai and MFP key figures on Wednesday was not an invitation for the MFP to join the coalition.
Paetongtarn Shinawatra, a Pheu Thai prime ministerial candidate and daughter of fugitive former prime minister Thaksin Shinawatra, also attended.
Most MFP supporters do not approve of the party voting for a PM candidate from Pheu Thai, according to the MFP. It cited internal opinion polls by its MPs showing 95% of supporters are against such a move.
Wiroj Lakkhanaadisorn, an MFP list-MP, posted on Facebook the party must not open a door for the return of a dictatorship.
He was referring to the "uncle" parties: the PPRP led by Deputy Prime Minister Gen Prawit Wongsuwon, and the UTN, which has PM Prayut Chan-o-cha as its candidate.
His remark came amid rumours either, or both parties would be invited to join the Pheu Thai-led coalition.