Couple of different parts to put together.
Wizard (Bladesinger) can give you a very nice boost IF you want light armor and have a good Int. From there how much wizard you take is negotiable. But remember that you can cast in any armor you are proficient in, so that's not your only choice. Also, it's power are not always on, and depending on DM and short rests may miss a lot of combats.
(Heavy armor class) / Wizard (Abjurer) can wear any armor and casting defensive spells like shield or absorb elements give an arcane ward which is basically a temp HP bank.
Bard (Valor) gives extra attack and full casting and buffing all by itself.
Sorcerer (Shadow) from UA: Underdark at 1st level gives a Con save vs. getting reduced to 0 HPs. Sorcerers have Con as a trained save.
A wildshaped Druid might be considered a variant gish. And can cast Shillelagh when not changed.
A Warlock (Tome) can also cast Shillelagh, using Chr. With the new attack cantrips in SCAG that can make them a better gish then Warlock (Blade).
Talking about Warlock and the cantrips, form that UA: Underdark comes the Undying Light patron which has +Chr to Fire/Radiant, which boosts those cantrips. Also has Fireshield (good gish spells) added to the warlock list. And yes, you can be a Tome Warlock with the Undying Light as a Patron.
Paladin 2 can very efficiently spell low level spell slots for a damage boost that works with any melee attack, including those given by the new cantrips.
If you are going up fighter, I'm still not convinced pure EK is worth it considering how slow you advance casting. But depending if you are taking a full spellcasting class it can grant you some spells like shield you wouldn't get otherwise.
Paladin and (Bard or Warlock or Sorcerer) fit together nicely with Chr, but you will still need Str 13 to multiclass paladin. At that point, it might be viable to do a heavy armor Str/Chr gish instead of the more common light armor Dex/[casting stat].