The way I'm structuring this is by giving each branch a collection of chapters that form into an arc before moving on to another branch. When outlining scenes, chapters, and arcs I explicitly write out what each are suppose to accomplish so I don't have fluff subplots, or character interactions that neither advance the story, nor advance a characterization. Every scene is meant to produce a certain feel and add to either the plot or help define characters, events, or settings (showing instead of telling).
It sounds like you have planned the structure in advance, and are aware of potential pitfalls so you are taking extra care to be clear with the various goals and characters within your parallel plotlines (I would not use the term "branching" as that implies a Choose Your Own Adventure or interactive narrative where some paths are taken while others are not, but I understand that you mean the 3 groups come together and diverge throughout the course of the story).
Planning ahead is the best you can possibly do until you actually write it. Then you will be looking at tonal shift, narrative dissonance, personality creep, and character redundancy – issues that may not be evident until you have more of the parts substantially written. Then you can actually read how well they segue or juxtapose to the next segment.
I had a long overlapping saga with several redundant moments that unintentionally recycled near-identical set-up and resolutions. I'd intended it as recurring theme or "echo", but as I blocked the scene again I realized it wasn't adding anything new. The subsequent scenes needed to evolve so they became more emotionally complex (even if these characters haven't seen it before, the reader has), or just do it once with the right character.
You mention giving each "plot" several chapters at a time. I suggest allowing each story segment some "closure", with a full arc that ties up the immediate loose ends – at least in the early part of the novel. Save the cliffhangers and characters wrestling with big unresolved questions for later in the story once the reader is more invested. If one plot breaks off on a cliffhanger then I read 3 chapters about a second team, but come back to learn the first group of characters are still in that same predicament, I'm going to get confused about the passage of time when I am away from a group. Eventually you can make the segments tighter and even go back to redo a scene from another perspective (Rashomon-style), but in the early part of the narrative I think it will be stronger to give each plot an emotional resolution before putting it on the shelf.
In my saga, I have two distant locations with two complete sets of characters. I've added in the passage of time while the narrative is "away" – when I return to earlier characters time has progressed by several days or weeks, but more or less on the emotional trajectory where they left off. Since the two plots run in parallel without much crossover or communication, I have the freedom to choose how and when to cut. It didn't end up cutting into evenly balanced segments like I'd hoped, but the cuts felt logical. I ended up with a primary plot with more action and a secondary plot with more pondering and soul-searching, but giving each segment its due and tying up the immediate loose ends made each transition feel like it was "ready".
You won't know for sure that your readers will follow all of your story until you get feedback from beta readers, but don't under-estimate how your readers are already multitasking in real life, and will be able to follow multiple storylines with varied relationships, tones, and motives. It's the smaller plot details, the disposable MacGuffins and emotional conflicts that drive a plot from point to point that the reader will forget – all the more reason to bring each segment to a resolution so these details won't need to be remembered while that story is suspended.
My advice: Tell each segment in its turn without distraction from the other parts. Rather than a 3-ring circus with simultaneous performances competing for attention, let each take the spotlight and be the only important story at that moment. Your readers should have no problem following the leap from story to story, and it will feel less like a gimmick and more like a natural narrative flow.
EDIT: (from comments)
The stories should interlock, eventually there are connecting threads between them all, but I mean more of bringing the emotional moment to a rest or plateau, so we aren't nagged by that hanging emotion when the focus should turn to the new section. It's more a "feeling" that that segment is complete, rather than an endless series of TO BE CONTINUED cliffhangers competing for attention as the "most important thing right now" to keep the reader on the edge of their seat
I'm suggesting to NOT put cliffhangers in the first few rounds. Instead let those early rounds feel like emotionally complete stories, so the first time we step away from them they are not lingering and competing for attention ("Wait, I have another 68 pages and 2 other plots before I know if she survived falling out the window???") Do that too early and the reader will say "so what". But take these characters through a couple of "complete" story turns, and it is more like returning to an old friend
