Most everyone on the internet is familiar with Alexandrian's three clue rule. The stipulation of that rule is that players are likely to miss some of your prepped content, which also includes any given clue. So to give the players a decent chance of progressing through a investigation-adventure, you need more than one clue leading to the conclusion, or to any breakthroughs that eventually lead to the conclusion. True to its name, the rule states that the perfect number of clues for each breakthrough is three.
I like this rule, for two reasons.
First, it means that each breakthrough is overdetermined: there is more than one path leading you there. This, to me, was a central thing in Masks of Nyarlathotep. You had a hunch from the beginning that you were going to Africa, but it felt very distant and hard to justify - what were you going to do there? With each new clue, you became more and more confident that you were actually going to Africa, up until the point where it seemed like the only reasonable thing to do. So basically, each new clue reinforces those you already have. Maybe you were already sure that Mr Vardis was a killer, but confronting him at this point seemed to carry so high costs. And then you learn that he is about to strike again, and suddenly acting becomes more urgent.
Second, and conversely, it also gives the adventure a branching structure. As there are always too many leads to follow up, the players will have to prioritize and consider what-if scenarios. Once the killer is caught they have perhaps seen 75% of your prep, so they still might not know what was the deal with Mr Vardis' prize-winning kennel. This makes the world seem bigger and the mystery more engaging.
In sum, the three-clue rule recasts a linear adventure to a dungeon-structure, where clues lead to new locations and breakthroughs in the investigation much like doors and corridors lead to new rooms.
However, this also shows some problems with the three-clue rule.
If we take the dungeon analogy seriously, we should accept that it isn't just a version of a linear adventure. Most dungeons don't have a straight-line progression to the end. And most dungeons are ok with you not reaching the end. If we were to apply these aspects of dungeon design, there would not always be three clues leading to the next revelation. Often there might just be one, and sometimes it would be hidden. And if the PCs don't find it they'll have to backtrack or even give up. And other times there would be clues that lead more than one step ahead in the investigation. So instead of 3 clues leading to A where 3 new clues lead to B etc, you'd have something more akin to a web.
However, even if we switch up our three clue investigation in this way - making sure that there are not just clues leading from A to B but also clues from B to A and from A to B via X and Y - we run into the problem of direction. Once you've reached C, it makes little sense to return to A because C is closer to the final conclusion than A. This is the same as in a dungeon, where you progress from the point of entry towards the central treasure through deeper and deeper levels.
If you want an even greater level of freedom in your investigation, your clues must be meaningful even in the presence of other clues. This is the rationale behind the guess-who structure and the triangulation (or venn-structure, as Kyana pointed out), described earlier. Here, all clues carry equal weight so as long as you're still uncertain about the solution, you gain from seeking and finding new clues.
For this type of investigation, I'd like to propose another rule for clues: the clue probability rule.
For each conclusion that you want the PCs to make, include a clue that they have a probability of finding whenever they make an effort to find it.
Say that you have a murder weapon: a knife with a easily recognizable look that would lead you to the smith who made it whom in turn could provide a list of clients. The knife must be somewhere. So we decide that it is in the pond, close to the scene of murder. Now if the PCs would look in the pond, they would definitely find it. So the clue probability is 100%. But perhaps they don't, because how would they guess that it is there? Instead, they might investigate the wounds. They can determine it's a knife without problem, but could they also conclude that this type of knife is made by Brambly the smith? I dunno. 1 in 6. Otherwise they just learn that the knife must have curious proportions. So maybe they ask a smith, or an assassin for help. 1 in 3. Or ask witnesses. 50% chance. The scrap-finder kids or pawn shops? 10% per day has passed since the murder. And so on.
The point here is that instead of designing several clues leading to the same conclusion (or in addition to), you design a clue that there's always a chance of finding whenever the characters make an effort to find it.
So now we have a hierarchy of blueprints for investigation adventuresThe linear structure. A breadcrumb trail where A leads to B leads to C. Fail-safe if clues are not hidden behind roll to continue. Very little agency, built in story arc.
The three clue structure. A breadcrumb trail where multiple clues lead from A to B and multiple clues from B to C. Almost fail safe, given the plurality of clues to each conclusion. Some agency, allows for story arc.
The dungeon structure. A web of breadcrumb trails leading between A, B and C through multiple clues. Failure is unlikely. Good agency, story is largely emergent.
The open structure. A limited set of clues of equal (or similar) importance, which can be found through many different approaches. Failure is possible. High agency, no story arc.