Utility
+1ing Taunt, pretty much everybody's talked about its merits and I don't think there's much else for me to add. The main thing I would like to emphasize how great it is that it can deny recovery, especially if we're pairing this with hazards or other options to accumulate damage against our natural checks. It just keeps CAP 31 afloat and lets its damage stick; it feels like a no-brainer. I do agree it should be an optional move, though, as it feels like something that more augments its kit on bulkier sets as opposed to something CAP 31 should be centered around using to find value.
I +1 Stealth Rock and Spikes to a lesser extent, and think at least the former is worth adding because most Ground-types available have access to the option, and having Stealth Rock means that we'll be able to explore the same Defog interactions that other key Ground-types share with Corviknight, with a positive matchup going into Tornadus-T/Zapdos being potentially of note. I don't think they'll at all be fixtures of its gameplan, but giving it a setting option does diversify potential team applications, and considering that Zapdos and Tornadus-T are both pretty good removal options, Diamond Storm remains a pretty strong option to have to tip the scales in CAP 31's favor as a setter. I prefer Stealth Rock since it means potentially more chip against Corviknight.
Hazard Removal I couldn't really care less for, and honestly don't really think is an avenue worth pursuing. Considering we'll be playing quite a bit into Corviknight and Landorus-T who will clear hazards regardless, I struggle to really see what value it'll give us unless our damage output is consistently reliable into both of them to a point where their use of Defog is deterred.
I'm indifferent on Toxic; it's a flexible, but not defining option that performs nicely as a midground for Pokemon that are going to be naturally much less afraid to come into CAP 31, putting pressure against Landorus-T, Slowbro, and Buzzwole specifically while letting it be more deliberate with Diamond Storm PP. Much like Stealth Rock, it's not something I see being a natural fixture into its gameplan, aside from letting CAP 31 focus more on outlasting Toxic-prone checks, but does provide an ease-of-use option that gives it opportunities to find value against bulkier structures willing to take its onslaught of attacks. It also feels like an option that would shine a lot more if we opt for 50% recovery, letting it take a war of attrition route, but with Pain Split it seems a bit unideal and messy to work with. Venomicon existing most certainly incentivizes it to hold onto Diamond Storm here, if nothing else.
Speaking of status, I'd like to invite Glare (but more realistically, Thunder Wave) to discussion. While Thunder Wave was briefly mentioned and would definitely be a more balanced option if Glare is too strong, I do think having a status-setting option that can, indiscriminately, cripple a great amount of its checks, including Corviknight, potentially Ground-types depending on the move, and really any Pokemon that isn't an Electric-type (which we have positive matchups into anyway) is an incredibly potent option into nearly all of its answers and, prominently, could help offensively diversify CAP 31 thanks to the speed reduction to open more offensive turns as well as the full paralysis chance to safely boost with Diamond Storm. It also has uses like letting it maintain its threat factor against more dedicated offensive structures to consistently pressure frailer breakers that may be willing to switch in once or twice, or more easily force switches by having the first move to break past them. Furthermore, paralysis is a potentially appealing option if we opt for Pain Split as recovery, since health would be more valuable by merit of Pain Split being fundamentally inconsistent, and paralysis would, usually, give CAP 31 the first move to keep its HP secure. I could see it being either too weak or too strong, but I think it's something worth thinking about.
Knock Off is a flexible option that feels like a less pro-concept variant of Toxic, which makes me lean against it more decisively. It punishes and makes progress against its checks, but does very little else aside from disruption and playing pretty much exclusively into a defensive niche that doesn't do much more than that, and doesn't really play to Diamond Storm's winning potential at all, unless you're removing a Choice Specs or Life Orb. If anything I would even argue it actively dissuades the use of Diamond Storm since you'll be having a move that naturally pressures airborne Pokemon with item disruption which also just so happens to cover other Pokemon that annoy CAP 31, which is huge given how strapped for slots CAP 31 already is. I can't really say I like it here at all.
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Coverage
As a general note here, I'd really like to quickly mention that, to get value, the coverage, to have incentive, has to have value in helping it expand and/or improve its matchup pool relative to its utility options. If CAP 31 is going to, on average, get more game-to-game value against most of its threats, which may include those that coverage would help against, through mechanisms like versatile status or Taunt over a given coverage option, then what's the point of giving it said coverage option? This is particularly important for CAP 31 considering that CAP 31 faces a unique conundrum where, despite us being super early into the moves stage, is already immensely strapped for moveslots, with two already being filled for STAB and Diamond Storm, and potentially another for recovery. That's why I think powerful coverage may be important if we want to particularly play into CAP 31's offensive potential.
Electric- and Ice-type coverage are an absolute nope from me. On paper, both types are amazing in helping it secure actually consistent and threatening matchups into Corviknight and Landorus-T respectively, but in practice, competing for a slot with Diamond Storm into Tornadus-T and Zapdos makes them incredibly volatile ideas relative to CAP 31's concept, as opposed to broken.
I'd like to be an advocate for Fire-type coverage. I know a lot of people have expressed distaste for it, but Fire-coverage locks some very specific matchups that are genuinely helpful for CAP 31 over utility while not making Diamond Storm even close to a moot option considering that Diamond Storm is a move that would be heavily preferred going into Tornadus-T and Zapdos. Obviously, Corviknight is a clear and major target, but being able to hit Buzzwole, Equilibra, and Ferrothorn is also of note considering all three are also rather unideal matchups that can readily block its progress in tandem with Corviknight. If the coverage is too perfect to some, I really liked spoo’s idea of specialized Special coverage as that also gives CAP 31 a much easier time blowing things like Buzzwole out of the water while maintaining a focus on its primary offensive moves and keeping Fire-coverage’s core merits. While it may also split its power some to a point of inefficiency, it would likely still consistently force Roost out of Corviknight, which is strong in and of itself in the context of this CAP. Despite that though I don't think physical coverage would be that bad considering the core type matchups Fire-type coverage excels at and is more mediocre into in comparison to Diamond Storm, especially with the secondary effect in mind, so long as we’re deliberate with what options we give it to ensure it wouldn’t be too much to handle.
Grass-type coverage is a cool idea, mostly because it safely locks the pressure against bulky Water-types that can't Scald CAP 31, but have absolutely no qualms in making progress in other ways, particularly in Slowbro and Tapu Fini's cases. The major appeal here is that alongside honoring Diamond Storm's appeal. I'd be for exploring it, but again, we're looking really strapped on moveslots, which in and of itself may make Grass-type coverage hard to afford, especially if we have utility that can pressure these Pokemon anyway. I think this option has a ton of merit if we want to play into optimizing CAP 31's already positive matchups, but depending on what utility CAP 31 packs, it may wind up situational, which makes me indifferent, but willing to see exploration on it.
Fighting-type coverage is fine. It mostly depends on what moves we opt for, with Close Combat and Body Press being of particular note. I think the main thing to consider is high pressure against Equilibra and Ferrothorn, with the ability to potentially force Roost against Corviknight. Though, again: if utility serves to help CAP 31 against these Pokemon as well as others, I feel it's probable it would drop Fighting-type coverage in favor of them considering the sheer importance of CAP 31's moveslots, but since utility gets less value into these targets than others, it feels decently likely to be a practical pick anyway.