3d6

This is just terrible.

I could maybe see a reason to stack multiple spellcasting classes, e.g. Sorc 1 (Con saves, spell slots, Subclass feature, Silvery Barbs) -> Order Cleric 1 (Heavy Armor, Voice of Authority, more spell slots) -> Wizard 1 (Rituals, more spell slots) -> Warlock 1 (Subclass feature, short rest pact slot, Armor of Agathys) -> Bard 1 (more spell slots) -> Druid 1 (more spell slots) -> Artificer 1 (more spell slots). That gets you to be a 6th level spellcaster and 1st level warlock in terms of spell slots, which you spend on things like Healing Word, Bless, Silvery Barbs, etc to proc Voice of Authority. Out of combat you cast a bunch of 1st level rituals and pretty much all the cantrips. Go with a +4 race that nets you 25ft move speed in heavy armor (Fleet of Foot Wood Half Elf or Mountain Dwarf), upcast Armor of Agathys to 3rd level, and go wade into melee, being obnoxious and begging to get hit.

Make sure you die before you hit level 8, b/c the martial classes offer you nothing with only 1 level each. If you do somehow survive and have to take them anyway, go for Rogue & Fighter first (Sneak attack and fighting style, probably Archery, to sometimes be able to hit with a ranged weapon), then Barb (big hit die, since you're committed to not dying), Ranger (Expertise), Paladin, and finally Monk (the saddest of all capstones).

There are many good reasons that almost nobody actually tries to do this in a real game. Sacrificing some mechanical optimization for flavor and sticking to a particular concept is one thing, but if you're going into more than three classes total you're either aiming for some sort of hyper specific niche build (which is probably still going to include multiple levels in most of it's classes even if there are four of them) or "lOl So RaNdOm" idiocy that's just going to result in a ridiculously incompetent character compared to any other PCs that are single or dual class.

I'll give an honest try.

Your build will rely heavily on magic items and a cooperative DM. That's 1 uncommon at level 1, a rare at level 5, and a very rare at level 11.

Custom lineage 13/13/8/13/13/14(+2) Feat: Resilient Wisdom (the only feat you'll get so it should be this)

Magic item: Cloak of Elvenkind (for hiding)

1. Sorcerer, Aberrant mind - Gets CON/CHA saves. Con is good for when people hand you scrolls to concentrate on and CHA is the only thing you're good at. Has mind sliver (to support your allies' actually useful spells) and dissonant wispers to chase things away. Can telepathically talk. Also take shield, silvery barbs, and chromatic orb. Stay away from the front, hide, and pray.

2. Rogue - expertise in stealth and perception. At least you can be a scout with your hiding and telepathy.

3. Cleric, order - heavy armor and you can let your stronger allies attack more with voice of authority. Also grab healing word.

4. Bard - more caster progression and some d8's to help your friends. Tasha's hideous laughter might do well long term.

5. Warlock, hexblade - in case you really need to hit something with a rapier, now you can use CHA

Magic item: Amulet of Health (suddenly you can be a frontline distraction!)

At this point things aren't too bad. You can scout or shield/rapier with 20 AC, +1d6 sneak, upcast dissonant whispers/chromatic orb, and support your friends a little with silvery barbs/d8s/mind sliver. Sadly, out side of more slots and some hp you start getting nothing from here on out.

6. Wizard - full caster, get utility spells

7. Druid - full caster, utility

8. Artificer - half caster

9. Ranger - half caster

10. Paladin - half caster

11. Barbarian - d12 hp

Magic item: +3 amulet of of the devout (gives +3 to all spell DC's and spell attacks)

12. Fighter - d10 hp

13. Monk - yey

It's interesting because you don't want the level 13 end concept, so the question becomes how the power level compares to normal progression? Obviously the first level is the same since you can't multiclass, but at some point this is going to drop way off. I'm not sure at what point.

I think the biggest problem is that you'll have to be incredibly mediocre in all your abilities: even with +3 ASIs from race, point buy can only get you straight 13s, and while you could theoretically delay some abilities through ASIs, you pay extra in point buy past 13 (versus ASIs which are all equivalent).

You could probably set up an Eldritch Blast character with a bunch of utility cantrips, but making attacks with a +1 bonus is going to be agonizing, unlike your damage since you can't take Agonizing Blast. You'll scale with level but it'll drop off pretty quick, since one level in lock keeps you behind on damage and you'll never get the splashier spells more focused characters will.