The highest possible permanent Spell Save DC is 28
The Character
Chad is a Level 17+ character with at least one level in warlock and these magic items:
- Robe of the Archmagi
- Rod of the Pact Keeper (only applies to your warlock spells)
- Ioun Stone of Mastery
- Tome of Leadership and Influence
The Calculation
+8 | Base Score
+6 | Level 17+ Proficiency
+1 | Ioun Stone of Mastery (Proficiency increase)
+2 | Robe of the Archmagi
+7 | 24 Charisma (acquired in specific Adventure Module, see below if okay with spoilers)
+1 | +2 Charisma (Tome of Leadership and Influence1)
+3 | Rod of the Pact Keeper
This involves...
[the Maze Engine from Out of the Abyss (188) which says:]
On each of the engines turns, roll a d100 and consult the Maze Engine Effects table to determine what the engine does.
[...]
36-49 | Loud whispers emanate from the hollow interior of the engine. Each character in direct contact with the engine can increase one ability score of his or her choice by 2, to a maximum of 24
Rulings
1 You can only use one Tome/Manual of any one kind on a character in Adventurer's League (DDAL FAQ v7.1 p. 8)
Jeremy Crawford unofficially tweeted that this works for wands, though the rules do not mention it.
Since the only hint (apart from their names) that magical rods, wands and staves can be used as foci are their tags rod, wand and staff that classify them as such, then we look at their tags descriptions at pages 139-140 of DMG but as you previously said, there is no explicit information about their use as arcane foci.
However, according to Jeremy Crawford, any wand can be used as an arcane focus. I can't see a reason why it wouldn't also apply for rods and staves since they usually are also foci but none of them had it written on their descriptions.
@JeremyECrawford Can Wand of the War mage be an arcane focus? Doesn't specify, and while wands can be foci, it's not clear that ANY wand can
JC: Any wand can be used as an arcane focus.
Jeremy Crawford tweets are no longer official rulings; only those in the Sage Advice Compendium are. However, the SAC does not provide satisfactory answer on this subject, so Crawford's tweet does indicate the designer's opinion on the matter, for what is worth.
The descriptions of DMG magic items are not exhaustive.
Marq commented:
An arcane focus is defined as "a special item ... designed to channel the power of arcane spells". Magic items of the "rod" category are "typically made of metal, wood, or bone ... about 2 or 3 feet long, 1 inch thick, and 2 to 5 pounds." Not all mundane rods of those dimensions are arcane foci (some may be, for example, cart axles, or crowbars); thus not all magic rods are. In contrast, all swords are weapons, by definition; it's not a special subcategory of swords that are made for attacking
First, I wouldn't call magic rods and staves something mundane; they are magical.
Second, the DMG magic items descriptions (p139-140) don't describe their every function, they do not specify their most basic functions since magic wands have nothing written there that they can be used as foci as weapons doesn't say that they can be used to attack. The same thing about rods and staves that doesn't explicitly say about their use as foci. RAW is the same to say that I can use a normal sword to cut someone but I can't use a Dancing Sword to do the same because isn't written that I can unless I make it fly while in my hand it doesn't have the capability to injure anyone. That would be unreasonable.
PHB also doesn't help.
There are no non-foci rods or wands described in the PHB. Would all rods and wands in existence be foci? That would also be unreasonable since it clearly says they are specially prepared to be used as such. If you imply that someone could make a non-foci rod with a log to support a broken table or a non-magical wand with silver and jade for a teacher to point at the blackboard because it's reasonable but isn't written in the book, then someone can make an ornamental sword that isn't a weapon and also isn't written there. Just because isn't written in the book doesn't mean it can't be done.
Marq said in his answer:
Magic items that can be used as a spellcasting focus, such as a hat of wizardry, say so explicitly:
This antiquated, cone-shaped hat is adorned with gold crescent moons and stars. While you are wearing it, you gain the following benefits:
- You can use the hat as a spellcasting focus for your wizard spells.
Unlike wands, staves and rods, hats are not usually arcane foci. If a specific item that usually doesn't have such function now works as such, obviously it need to be stated in its description. That's the reason the hat of wizardry clearly have it noted there. Since wands, rods and staves are meant to be used as foci as much as weapons are meant to be used to attack, they didn't need to have it noted in their entries; it's their basic function, you just assume they do what they are supposed to do.
Best Answer
Probably Not
Increased Spell DC is, as you've said, very hard to find. The lack is probably due to the bounded accuracy of 5e, but the fact that it's so rare to find something to boost it is an indicator that doing so homebrew may be dangerous.
Increasing DC is generally accounted for by the increasing proficiency as you Level. While some items can force Disadvantage on a save (like a Bardic Instrument for Charm Spells), that is balanced by having a lot of enemies immune to charm or resistant to magical effects (advantage on their saves.)
An illusionist is a tricky situation. Many of their spells are either Intelligence saves (so magical resistance still works, but against INT, which is generally a lower stat for many creatures) or Investigation(INT) checks (which very few have any proficiency in.)
ASIs and Assumptions
I am assuming that this level 15 character has maxed out their Spellcasting modifier to 20/+5(charisma for the Sorcerer.) If maxed out, the only Magic Items that increase his Spell Save DC are the Tome of Leadership and Influence (Very Rare) which increases their Charisma and Charisma Max by +2 and the Robe of Archmagi(Legendary, only for Walrocks, Sorcerers, and Wizards) which increases Spell Save DC by 2.
In addition, allowing a straight +2 to DC without increasing the Spellcasting Ability could create an odd situation where your Ability Modifier for DC is different, and greater than(!), the maximum modifier for ability scores. An example of this would be either a max 20 Ability score generating a +5 modifier, except for DCs which would turn it to +7. Or a situation where someone has a Headband of Intellect which increases their Int to 19. That should generate a +4 Ability score modifier, but instead it would end up being +6, which is the equivalent of 22 Intelligence.
Other Ideas
My table uses the Variant rule in the DMG for Proficiency Dice (DMG, 263). It makes that DC swingy (could be lower than normal, could be higher), but it adds a neat effect to the DC set. And you get to roll (more) dice.
You could also look at creating a homebrew feat. Maybe give him a couple more illusion spells and allow a 1/SR ability to force disadvantage on the first save/check against an illusion? I had a feat like that for one of my characters that focused on illusions and it did make them a bit more interesting. However, illusions are very table dependent and the power of this will vary. For us, we allow illusions to impart conditions, so this gave my illusions a big boost without a huge downside. We still try to play the monsters reasonably and also balance "we're not removing this monster from the entire battle with a low level illusion spell" with "let's make this more fun"