Paths to Character Routes
From my experience with visual novels in the genre of romance, games with multiple endings generally divide themselves into player-aware and player-unaware systems, the former being systems where the player consciously chooses who to pursue, and the latter being the player finding out whom their choices will pair them up with. For lack of better terminology, let us call these pursuit and matchmaking systems.
To clarify, a pursuit system would be one that directly lets the player character choose who they will end up with, either by allowing the player decide who to spend time with or by letting the player character choose who to hire/befriend/tell their dying wish to.
The first, and more common, type of pursuit system usually starts with an intro, where the main obtainable characters are introduced in some fashion, and then the story splits off into different paths depending on player choice. In these branches of story, the other, unchosen characters are usually seen very little or not seen at all. The choices after the split are purely to decide which level of ending the player will obtain with the chosen character. You can tell apart a Type 1 from a Type 2 by looking at its walkthrough. If the paths are listed in ascending order by number of choices, or if some paths truncate and end abruptly before major plot elements (e.g. chapter breaks) then it is most likely a Type 1 pursuit system. A notable example is G-Senjou no Maou (https://vndb.org/v211)
The second type of pursuit system is a little more uncommon, and is nearly the complete opposite of the first. Instead of an intro that schisms into separate paths, the entire story can be experienced- racking up points with various characters, interacting with everyone- but then at the end the player makes a choice as to which ending they want to see. There are many variants of Type 2, but all of them have the same basic premise that the player chooses who they want to pursue, but is still given a chance to explore and interact with other characters. Generally, the character that has been interacted with the most is the one whose route the player character will end up on, and there may or may not be thresholds involved. Notable examples are Re:Alistar++ (http://www.sakevisual.com/realistair/) and Heartstring Bugs (http://unbrokenhours.com/hsb/).
A matchmaking system, on the other hand, focuses much more on placing the player character with an obtainable character in a single story setting. Instead of splitting off of the main story, it sticks very closely to it. This style of storytelling is similar to Type 2 of the pursuit system, but the main difference is that the player has no idea what to do to obtain a particular person on their first playthrough without a guide or walkthrough of some sort. Choices that are presented may be in the fashion of “What should I wear today?” or “What direction should I start walking in?” or “What food do I like to eat?” The game is interested in matching the player character’s personality to one of the obtainable characters, hence the word “matchmaking”. The results of choices are not immediately obvious, and it may be difficult to get a certain ending without the help of a walkthrough. Notable examples of this system are any of the Fantasia games (http://mementomori.vnovel.com/released-games).
Of course, there are also systems that lie somewhere between player-aware and player-unaware. Player-partially aware, or Dual Type, if you will, that has some elements of player choice (romantic partner chosen by player) mixed with some elements of player discovery (romantic partner chosen for player). The most common example of Dual Type is a game that has multiple characters where the results of choices are not very obvious (e.g., “Choose what food to cook!”) and where a good portion of the game is spent racking points up with multiple characters. The characters whose points exceed a certain ‘threshold’ are then presented to the player in the form of a choice and the player is allowed to choose whose route to follow. Typically, the points racked up after that split are used to determine a good/bad/true ending. This is similar to a matchmaking system, except for the fact that the player is given a choice as to which route to follow instead of being forcibly placed on one. The closest descriptor for this variant would be a Pursuit Type 2 whose beginning choices got swapped for matchmaker-type choices. I’m going to reference another Unbroken Hours game here, Frozen Essence (http://unbrokenhours.com/fe/) is a good example of this particular variant of Dual Type.
That said, there might be some that I am missing. But as complete/incomplete as this article is, hopefully it will help you decide what kind of branching behavior you want to pursue in your projects.