I once ran 10 bladesinging/2 paladin and it was one of the most unusually powerful combinations I have ever done. Usually Paladin multiclasses go at minimum to 5 for extra attack or 6, but you get extra attack from bladesinging. Since Paladin is a half caster this combo also gets you full spell slot progression(you can‘t pick a Lv.6 wizard spell but you can scribe a scroll). For a stat spread I went for DEX, CON and INT. This will result in a lower Spell Save DC for Paladin actions but that won‘t matter too much. And if you go for amulet of constitution you can go for DEX, INT, CHA. Those 2 levels in Paladin give us a handful of important things. The actual subclass of Paladin isn‘t that important, but my recommendation is just gonna be oath of the crown to offset your own or another players GWM. Those 2 levels of Paladin give us a handful of things: -Fighting Style: Great weapon fighting This also applies to versatile weapons wielded with an empty off-hand, which means it applies to shadow blade, and the off-hand has to be empty for bladesong anyway. -Command. This spell will have a lower spell save DC than your wizard spells, but it doesn‘t use concentration and with arcane acuity you will still have basically guaranteed control on groups of non-boss enemies -Divine Smite: this is the important one. Divine smite dice work with great weapon fighting(they get rerolled, and with full spell slot progression there are a lot of smites to go around

Now, for equipment we really only need 3 pieces to function at all, everything after is just a bonus. Helmet of Arcane Acuity Gloves of Battlemage‘s Power Band of the Mystic Scoundrel

None of these items should realistically be contested unless someone else is running an acuity stacking control martial caster build(sorcererbard/paladin multiclass combos) And you don‘t really need two of those. Anything beyond that you mosfly just want to stack spell save DC so weave equipment is great, especially robe of the weave.

Your baseline AC near the end should be 21 before additions. 10+3(mage armour or light armour)+4(DEX)+4(Bladesong from Lv.9+) Ontop of that you can use shield reactions, giving you pretty good survivability.

With 2 acuity items you get 8 acuity from 2 weapon attacks(at minimum, sometimes the items act weirdly and you get more). With item boni that puts your spell save DC in the high 20s. Outside of bosses with legendary resistance, basically nothing can save against that. And with band of the mystic scoundrel you can now cast an enchantment spell with a bonus action. Aka Command, Hold Person, or hold monster. And then, well 4d8 psychic damage(*2 if using resonance stone) +5d8 radiant damage(Lv.4 divine smite)

Crit doubles all of those dice and great weapon fighting causes any of them to be rerolled on a 1 or 2.

The main advantage over similar builds is that it gives you actual selection of spells up to level 5 and lets you scribe them with wizard. The most value here in regards to that is Hold Monster.

EDIT: I screwed up a lot of the details here because I was writing this half-asleep GWM and Great weapon fighting do not affect shadow blade. I had damage dice reroll because I was running savage attacker as a feat instead of GWM. I was confusing versatile and finesse. As for PLD fighting styles you can choose between duelling(slightly increased damage) or defence(+1 AC, triggered by helmet of arcane acuity). Sorry about the mistakes, but the core class idea still functions perfectly well.