I wanted to add some thematics to go along with the mathematics when considering which frames would be good witch frames.
Without considering Invocation mods, I've come up with a small list:
Wisp the Windwalker - with Lohk Canticle, Lethal Torrent and Arcane Velocity, fire rates up to +210% are attainable; add in a speed mote and 250-300% plus fire rate is achievable.
When considering multishot, Lethal Torrent and Galvanized Diffusion can effectively triple your modded "rate of fire" for ridiculous amounts of Magic Missiles being launched in a short time span.
Miarge; Mistress Malkavian - Hall of Mirrors allows additional primary AND secondary projectiles, multiplying the multishot of both modes and expanding the potential radius of both radial attacks. Although not as fast as Wisp (no motes), it's still quick, puts out a lot of bolts and covers a slightly larger area.
Witch Queen Saryn - Venom Dose and Toxic Lash provide Corrosive and separate Toxic damage, Accelerated Isotope gives you Rads; mod for Viral and you keep Electric as a freebie. Five damage/status types that can be used for Galvanized Shot. Ability Strength now plays into your Grimoire's damage and can be further enchanted by infusing Roar into the build. Words may not leap off the page as verbose as with the prior builds but they will have deep definition.
Harrow the Heretic - Does he even need a Grimoire? Sure, why not. Like Wisp, Harrow can get the fire rate up to a similar pace as well as allowing the tome to generate health and energy while pushing out the crits. Question is, what is your preferred infusion for such a well rounded frame? Nourish? Gloom?
DeathChilde Yareli - Infuse Airburst (w/Airburst Rounds); group, Sea Snare to immobilize, slow, DoT and soften up the mob, then strafe with blade and tome on the back of a wild sea creature. Cold, Slash, Electric, Rads, Viral; feed your Galvanized Shot; ramp up your Galvanized Diffusion.
I know there's a Nekros and Gyre in there somewhere but it's late and I'm tired, lol... good night.