Increase the BWD for DPS formula: WD%, ED%, ED+, WD+, WIQ , Power and maybe even APS. Also Empower Talent , Focus Talent, Might and even Astral. Permafrost and Inferno for fire and ice.
Increase MH% DMG and/ or OH% DMG:
Identity, Push the Limit, Hero points of a skill, All skills affix for adding hero point to skill if you're different class, Multi Attack and Extra Attack. Hit frequency to increase hits of skill per second. Mutilate Talent too. Also including Timewarp and Cosmic power.
Glasscannon, Barbarian, DMG to Elites, DMG per Pierced, Total DMG%, Equality, Defiant, Pathfinder, Angelic, Demonic, Relentless, Amplify, Living Force, Momentum, Bloodmagic, Energy, Fury, Alchemy, Crit DMG, Deadly Strike to crits, Brutal , Exposed, Ruptured, Darkness , Adventurer, Arcanist, Haunting Bonus, Epiphany Bonus , Ballista, Buccaneer, Malestrom / Mayhem .
DMG for multiple enemies with ice or poison: Plagued, Druidic and Frozen.
Weaken , Effective and Ascendant, a way to deal DMG to normal as a different way to Ignore resist and usually a bit more than you can get with Ignore Resist if you have high enough Weaken.
Elemental crit dmg: The elemental crits itself and the legend affix for them like Blight for example.
Shock has stack debuff in itself to increase all DMG by 50% after 4 hits.
Poison has dot DMG and so does Fire. Also bleed.
Many ways to increase DMG, each with different conditions and methods.
Glasscannon and/or Barbarian as well as mythics like Brutal and resource mythics though are very common ways of increasing DMG for any build. Then sets like Defiant or so too.