Kesses MP Julius Rutto said the country was "facing a challenge" with the Constitution and that debate on whether or not the three offices should be created should be decided in a referendum.
"On the majority side, we came in promising not to expand the government. So we need to listen and take time on this and understand the petitioner. What point is he trying to drive home?" Mr Rutto said.
Mr Okul also seeks to alter the order of precedence observed in the National Assembly to that of Speaker, prime minister, and leader of opposition.
The creation of the PM post was also contained in the BBI proposals as part of efforts to expand the Executive and address the winner-take-all issue.
Mr Ogolla has drafted a Bill seeking to bar a deputy president from contesting for the presidency immediately after serving two terms.
The Constitution of Kenya 2010 (Amendment) Bill, 2022, is also pushing for creation of the post of opposition leader in the National Assembly.
The position will be held by the presidential candidate who comes second in a General Election, and whose political party or coalition of parties has at least 25 per cent of elected members.
The proposal is part of efforts to entrench the status of the opposition in law.
Under the banner "Operation Linda Ugatuzi", the new Bill seeks to alter the structure of the Executive, devolved units as well as strengthening the Independent Electoral and Boundaries Commission.
Although Mr Ogolla claims the opposition has no hand in his initiative, some components of the Bill have borrowed snippets from the flopped BBI.
"The window for reviewing the Constitution is already up and it is important to look at some issues through a popular initiative," he said.
But observers believe these new initiatives face a tough task becoming reality.
Violate the law
Waikwa Wanyoike, a constitutional lawyer and a political commentator, told The Standard that some of the proposed amendments violate the law.
"Most of the attempts that have been made to change the Constitution are not aimed at strengthening the Constitution because they are only targeting self-serving interests," he said.
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According to the analyst, the attempts are politically driven aimed at controlling and capturing power, and stand little chance of success because of how they are drafted.
"The proposals to bar parties from nominating a governor and a senator in the same county, for instance, violate the spirit of multi-party democracy," said Mr Wanyoike.
Clifford Otieno, another constitutional lawyer, however, says that some of the proposals deserve consideration because they seek to strengthen governance.
"The proposal to bar deputy presidents from succeeding their bosses immediately after serving two terms can help improve service delivery. You will find that deputy presidents are more preoccupied with planning how to succeed their bosses," said Mr Otieno.
The analysts believe the proposals must be put to the test in a referendum due to the rigidity of the Constitution, which means they will follow the BBI path and not the parliamentary route.