While more can always be written, and I encourage more information and answers, until then, you may be interested in this previous answer of mine to the question:

"It's often said that George Washington and other founding fathers were opposed to political parties. What did they propose instead, and did they try to encourage said alternative?"

The TL;DR is that there are competing interpretations, at least when it comes to George Washington:

One interpretation says that he believed in a sort of top-down approach. The president should set the political agenda and Congress shouldn't much question it, but just work toward achieving it.

The other interpretation is that he believed in more of a bottom-up approach. The president should act like a sort of referee between competing ideas, and then make a determination of which idea was better, and then everybody should support the president's decision.

More details can be found in that previous answer. Maybe someone else can chime in on John Adams' vision of how it might work.

Short answer: In the early United States, we went from having no party system to a two-party system (1789), to a dominant-party system (1800), to a one-party system (1816), to a multi-party system (1824), to a two-party system in a more stable equilibrium (1828, 1860).

The Constitution was written before a party system truly existed. And it was not written with a party system in mind. The same can be said of the Founders, who had a negative view of parties altogether, and certainly no expectations for the modern party monopoly. More than anything, the two-party system is an unintended consequence of single-choice, simple-majority voting. (In political science, this tendency is called Duverger's law.)

The party system broke down again in 1860, and became set in stone during the unspoken dark ages that follow the Civil War. The era of Reconstruction and sweatshop factory labor lends itself to a Gilded Age as far as money in politics. The vote-getting political machines that had first developed in the 1820's became indispensable tools of wealth and power, with 2 poorly distinguished pro-business parties by the late 1800's. To this day, the party monopoly exists because it answers to itself, and there is no democratic alternative.

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To put the Founders' ideologies in context, we have to consider their origins, and their own personal interests. This helps us understand the limits that were placed on the Constitutional Convention.

The ideas we have about Western democracy and representative government really grew out of the Enlightenment. But the Magna Carta, British Parliament—that's been around since the 13th century, as royalty would consult the nobility about this or that, & the question of taxes. The legislature was a feature of constitutional monarchy before we turned it into democracy.

This is also true of America ! — our colonial legislatures predate the Enlightenment, and they were largely controlled by the ruling class. We never had a nobility, but we still had a few rich families that were able to accumulate wealth and power over generations. They benefited from land grants spanning thousands of acres, & of course many of them pioneered their fortunes with forced labor, plantation systems supplied by human trafficking.

There was no great separation of wealth and political power when we were part of the British Empire. The ideals of the American Revolution are great because we denounced British royalty and proclaimed the rights of every free man, but it was a very narrow ideal in its original form.

The Revolution was supported by the ruling class and small farmers alike. But at the Constitutional Convention, as Charles Beard famously points out, the 55 delegates were all upper-class men. There were many plantation owners, but more than half of them were lawyers. And naturally, they did not think much of the poor tenant farmer or their slaves. If they did, the question of national unity swept that off the table. Natural rights were still associated with "life, liberty, and property," before Jefferson edited the phrase and lived in hypocrisy by it.

The United States is an incredibly stable and prosperous republic, but the original democracy was quite limited. When it was founded, the popular vote didn't truly exist, & you could not vote unless you owned land. Ultimately, the Constitution left the states to control their own elections, and the actual democratization of the election process had to be patched in on the state level in the 1820's.