This will break down the DC for every class and school (that matters). It makes some assumptions:
-Character is going for maximum DC's in that specific school. If you are not, reduce appropriately.
-Character is in the destiny which would provide maximum DC's. For WIS/CHA-casters this is Exalted Angel, and for INT-casters it is Magister/Draconic.
And some omissions:
-No unsustainable or unreliable buffs such as House D pots, Bard Songs (unless the caster is a bard), cookies, Joy of the Queen, etc.
-No Archmage wizard. I don't believe they actually gain any DC over Palemaster due to Lich-form and Harper Agent
-No multiclasses. Yes some builds can have slightly higher DC's, like 17Drd/3Brd or Monk Splash FvS, but that's just too complicated if we're trying to be comprehensive. Figure those builds out for yourself.
All sources of stat/DC are available in this spreadsheet. I encourage everyone to point out any mistakes I have made or things I have forgotten. I'm sure there's some, but I believe the errors are limited.
HERE IS THE SPREADSHEET FOR ALL MAXIMUM CASTER DC'S AT ALL LEVELS.
This image provides at-a-glance maximum DCs at a variety of levels.
Checklist for DC casters:
Build
20 starting (CHA: Drow, Dragonborn. INT: Drow, Gnome, Deep Gnome, Sun Elf. WIS: Deep Gnome)
All level up increases into your casting stat
Tome
Feats and Twists
Arcane Initiate (Wizard Past life, purchased)
Spell Focus [school]
Greater Spell Focus [school]
Epic Spell Focus [school]
Heighten Spell
Embolden Spell (does not apply to all spells, mostly evocations like Greater Shout and Burst of Glacial Wrath)
Scion of Air, Earth, Feywild, or Shadowfell
Bardic Dilettante Purchased past life feat (enchantment only)
Magister Tier 2
Draconic Tier 2 (Evocation/Conjuration only)
Buffs
Ship buffs (+2 stat and +1 DC amenities)
Yugo pot (75 Yugo favor to unlock vendor)
Stacking (Remnant turn-in potion)
Past lives
Racial past lives (CHA: Half-Elf and Dragonborn. INT: Gnome and Drow. WIS: Human. Two lives needed per race)
Racial completionist (complete thirty racial past lives, 3x in each)
Completionist (complete one heroic life on every class)
Epic Completionist (unlocks additional twist, proxy +1 to your casting stat)
Cleric past life 3x (Conuration)
Sorcerer past life 3x (Evocation)
Deep Gnome past life 3x (Illusion)
Gear
Enhancement bonus to stat (Cannith Crafted / lootgen until lvl28, then u36 items or Slavelord items)
Insight bonus to stat (Cannith Crafted / lootgen, named u35 item for CHA at lvl28)
Exceptional bonus to stat (augment starting at lvl20, Globe of True Imperial Blood, certain named items for lvl18 and 19)
Quality bonus to stat (heroic slavelords, some named items, certain named items starting at lvl28 or Slavelords for +4)
Profane bonus to stat (Executioner's Docent/Plate at lvl8, Litany of the Dead at 14, Epic Litany or ring from Black and Blue at 28)
Artifact bonus to stat (Heroic and Legendary Slavelord Sorcery set)
Reaper bonus to stat (named helms from reaper quests)
Alchemical bonus to stat (WIS only) (Alchemical / House C raid crafting)
Equipment bonus to DC (Cannith Crafting, named items)
Insight bonus to DC (Cannith Crafting, named items)
Quality bonus to DC (Heoric or Legendary Spinneret, Mutilator of Minds, other named items)
Artifact bonus to DC (Heroic and Legendary Slavelord Sorcery set
Profane bonus to DC (Thunderforged Armor)
Exceptional bonus to DC (Thunderforged 2-handed item) (not included in spreadsheet)
Festive bonus to stat (INT, WIS only) (Night Revels Augment, buy from other players)
Enhancement bonus to DC (Yellow augment, from The Twelve (+1) or Gianthold (+2))
Additional sources of DC:
All casters can benefit from Epic Deific Diadem, for +2 to all DC's. But, it interacts with different classes differently. Pale Masters can easily keep the bonus at +2 with Death Aura ticks, but a Druid who casts, say, Earthquake and then Storm of Vengeance, what bonus they have will be impossible to predict. Consider at your own discretion. Furthermore, it conflicts with a Reaper bonus hat, unless you have crazy luck and get a Reaper version of the Diadem.
Assuming two Epic feats are reserved for Epic Spell Focus and Embolden spell, Epic Stat and Stat Twists can give up to +7 to one stat. However, you will probably spend most of those points in other areas (e.g. Evocation/Conurjuation casters already have a twist reserved for tier2 Draconic). For ballpark figures, Wizard can normally afford +4 INT from these sources, and other classes will get +2 or +3 to their stats.
LGS tier3 gives +2 Exceptional to a stat, resulting in +1 over Globe of Blood, which could give +1 all DCs if this bumps you to an even score.
All casters, except Bard where it is already counted, can get +2 to DC's with Inspire Excellence and Spell Song Trance from a Bardic party member.
Arcane Archer tree comes with +4 to Enchantment DC's. Only Wizard has access to this though, through the Sun Elf AA tree. I don't know if there are enough points to invest very far into it.
Debuffs:
Not a complete list, but these are some useful ones.
No-save, AoE abilities:
-With Aura of Menace, FvS get effectively +2 to all DC's, passively, making up the difference between them and Cleric.
-With Mantle of the Icy Soul, Druid effectively gets +4 to DC's that target Fort and Ref on anything hit by their Cold spells.
-Druids also get Autumnal Susurrus, giving their Acid, Electric, and Negative spells a 40% chance to apply the shaken condition, which is -2 to saves. Storm of Vengeance and Call Lightning Storm are notable two AoE spells that can trigger it.
-By stacking Solid Fog and Waves of Exhaustion, Wiz and Sorc can debuff reflex saves by 7.
-Crushing Despair reduces will save by 5, even if mob makes it saves. Other spells like Hypnotism have a similar effect
-Bard's Insult from Swashbuckler reduces saves of a choice by 3
-Warlock's Taint the Blood from Soul Eater reduces fort saves by 4, after attacking a mob four times
No-save, single-target abilities;
-Exalted Angel's Shadows Upon You can provide up to -12 to saves. SUY -> Wizard PL Magic Missiles -> Finger/Destruct is efficient
-Magister's Spell School Augment gives 15% chance for Conj/Evoc | Enchant/Illu | Necro/Trans spells to lower Ref | Will | Fort saves by 5
-Energy Drain effectively gives -4d4 to saves. Enervation 2d4.
Save-based, AoE abilities:
-Crushing Despair gives another -2 if a mob fails its save against it
-Symbol of Pain gives -4 to saves if a mob fails its save against it
-Mind Fog gives -10 will saves if a mob fails its save against it
Save-based, single-target abilities:
-Inflict Curse gives -4 to saves
Secondary schools/build variance:
It is not possible to get these DC's in two schools at once. A secondary school will have a much lower DC. Furthermore, you may have to invest at least a little bit into spell pen, which could lower your DC's.
If you are not maxing a school, you will lose up to:
-3 from Magister tier2
-3 from 3x Spell Focus feats
-2 from appropriate legendary feat
-2 additionally if you do not have any of Scion of Earth, Air, Feywild, or Shadowfell
-3 for Illusion, if you use a race other than Gnome/Deep Gnome
-3 for CHA Evocation casters if they are not Dragonborn
-2 for Evo/Conj, from Draconic tier2
-1 for Enchantment, Bard PL feat
-1 additionally from Enchant if you're saving AP from racial Drow/Sun Elf tree
You will also lose more if your class provides DC through a multi-selector, such as cleric (who must choose +2 necro, +2 evoc, or +1 each).
It's also entirely possible that you will not be able to fit in all the DC-boosting equipment for a secondary school, or you will do something like not wear Thunderforged armor in favor of something that gives bonuses in other areas.
Obviously these all depend on your personal build choices. Also I assume a +7 tome which many people don't have. +5 is readily obtainable, though grindy, through 5k favor reward.
DC boosts:
For WIS/CHA casters, Exalted Angel's Ascendance ability gives an unlisted +2 to WIS and CHA, for +1 to DC's. Ascendance lasts two minutes and has a five minute cooldown, a respectable 40% uptime.
Arcane Insight gives +6 to DC's for 30 seconds. Three minute cooldown.
Magister can boost DC's by +5 for 20 seconds, but this only applies to INT casters. Five minute cooldown.
For Warlocks, the first core in Tainted Scholar gives +2 DC's for 20 seconds. One minute cooldown.
Harper Agent Tier5 has a passive +1 to all DC's, and also comes with 10 seconds of +10 to DC's. But it has a five minute cooldown, and conflicts with class trees.
Furry of the Wild's Acute Instincts gives +2 WIS, but requires drinking a Rage potion. This boost can be sustained indefinitely. It is already counted in the spreadsheet.