Build assumes Arcane Avenger in your warframe, removing the need for Crit Chance mods.

Elemental Coverage:
Saryn(all weapons): {Corrosive+Toxin}
Zenith: {IPS}+Corrosive+Cold
Kuva Nukor: {Radiation+Magnetic}+Viral+Heat
Contagion Zaw: {IPS+Viral+Blast}+Gas+Electric
{} = innate damage types.
Viral is used on KNukor because the Contagion explosion(the part that is Viral) doesn't reliably hit PT because of buggy hitboxes.
All combined elementals are covered by KNukor+Zaw, so Zenith can cover Corrosive, allowing you to skip casting Spores(Corrosive buff) during the first shield-phase, saving 1-2seconds(slow "cast") when speedrunning.

For runs without [Saryn]:
All 6 combined damage types are covered, but there's simply no way of covering all 4 base types with 3 weapons, because even if you subsume [Volt]'s Shock to buff, the Electric will just combine into other damage types. [Saryn]'s 3 is unique in that the Toxin damage doesn't combine into other types.
Also note that [Chroma] players can replace their +Damage mods with something else for more damage.

PT builds:
Saryn/Chroma/Wisp
Zenith
Kuva Nukor
Contagion Zaw
Mausolon
Smeeta(for credits)/Adarza(for speedruns)