Continuing with Madison's essay, he now tells us that, since "neither moral nor religious motives can be relied on as an adequate control" for faction, governmental structure must be relied upon to solve the problem.
And the structure he recommends? A republican form of government (elected representatives), a large country that would provide wide-ranging views on issues, and properly-sized districts from which representatives are elected. This structure, he argues, would refine and enlarge "the public views" of the nation and pass "them through the medium of a chosen body of citizens ... whose wisdom may best discern the true interest of their country, and whose patriotism and love of justice will be least likely to sacrifice it to temporary or partial considerations."
"Extend the sphere," "a greater variety of parties (factional groups) and interests," "less probable that a majority … will … invade the rights of other citizens," "more difficult for (that majority) … to discover their own strength, and to act in unison with each other" … as Madison's argument takes full strength, you can see that these are not statements in support of any coagulation of individuals.
Communication between representatives would be checked by a natural distrust of the motivations of the other representatives. This is not a bad thing; the Founders were studiously suspicious of human nature and they saw this as the way that self-interested representation would work. The belief here is clearly that individuals, by virtue of the government's structure, would be forced to compromise with other individuals for the public good.
The remedy for the problem of faction, then, is a special kind and size of republican government, one whose focus is self-interested individuals who represent as best they can the constituents of their districts, but find it "more difficult … to discover their own (collective) strength(s), and to act in unison with … other(s)."
As it oozed into the available crevases between the Founders' words, the modern political party eventually proved to be a successful effort to circumvent Madison’s remedy for faction. Party creates artificial lines of communication between individuals elected by separate electorates; it makes it easier for groups of these individual representatives to "discover their own strengths" and "to act in unison," both activities Madison found distasteful.
There is an argument that modern parties are amalgams of disparate factions that themselves smooth the edges off factionalism. Madison did not address that argument because modern parties did not exist at the time. But a reasonable review of history and current events proves the argument to be a red herring.
Modern political parties have a life of their own, so to speak, apart from the separate factions that comprise them. In that vein, parties act like singular factions, often with the voice of a controlling majority of party faithful that do comprise a single faction, and act singularly for the expressed benefit and furtherance of the party.
Time and again, representatives who should (according to Madison) be representing the constituencies of their districts, act solely in the interest of their party. Orchestrated non-votes, filibusters, shared bully pulpit language, committee pecking order games, … all of these are stupendous wastes of the public’s time and money, all in the interest of party.
The argument is also made that furtherance of the power of a party is, in fact, in the interest of the comprising factions. Precisely! Only ideologically-narrow factions believe that their interests match those of the general public. Madison argued 180 degrees opposite – that the interests of a faction were not equivalent to the public good.
Inspect the common activities of modern parties, and you clearly see the successors of the hated factions of Madison’s day. To ignore that "the public good is disregarded in the conflicts of rival parties" is to ignore historical fact.
Madison did not argue explicitly against modern parties; but he clearly argued against the kinds of activities they engage in.