Show me what that PC looks like at 5th level.
I'll then show you what a single classed Sorcerer, Fighter or Monk looks like at the same level.
We can compare your PC to those other three.
Assuming Halfling with the same stats and the second chance feat at 4th level. I bolded the things I think are really significant and put the comparative large weaknesses in red.
At 5th level this triple class character has:
16 base AC, 21 AC with shield, patient defense
32hps,
can Charisma save vs damage to keep from going to 0 hp
proficiency in Con and Charisma
Move 35
Darkvision 120 feet
6 spells (Silvery Barbs,
Shield as Sorcerer, Darkness, Darkvision, Pass Without Trace and Silence as a Monk)
2 1st level spell slots
5 cantrips
(BB, GFB, message Mage Hand as sorcerer, Minor Illusion as Monk)
0 sorcery points
3 ki
second wind 1d10+1
No Action Surge
Damage to 1 target using cantrip - 13 (18.5 to 2 targets) - (1d10 Warhammer, 1d8 GFB, 3Dex, 5.5 to second target)
Damage using attack action and martial arts - 16 (1d10 Warhammer+1d8 martial arts+6)
23.5 damage using flurry of blows (1d10+2d8+9).
patent defense, step of the wind, no stunning strike
5th level Sorcerer:
14 base AC, 19AC with shield, second chance
27 hps,
Can Charisma save vs damage to keep from going to 0 hp
proficiency in con and charisma
Move 25
Darkvision 120 feet
9 spell slots,
6 spells known plus darkness
5 cantrips
5 Sorcery Points
0 ki
no second wind
no action surge
Damage to 1 target using cantrip - 10 (15.5 to two targets) (1d4Dagger +1d8GFB+4Dex, 5.5 to 2nd target)
no martial arts, no FOB, no Monk spells, no stunning strike
5th level fighter
16 AC, 21 with shield, second chance
40hps
Proficiency in
Con and Str
Move 25
No darkvision
3 spell slots, 4 spells known (probably
shield, Absorb Elements, PEG, Silvery Barbs)
2 cantrips
0 sorcery points
0 ki
second wind 1d10+5
Action Surge
Damage to 1 target using cantrip - 13 (18.5 total to 2 targets) (1d8Rapier+1d8GFB+4Dex, 5.5 to 2nd target)
Damage attack action (extra attack) - 17 (2d8+8)
No martial arts or FOB
No Patient defense, no step of wind, no Monk spells, No stunning strike
5th level Monk
17 base AC, no shield, second chance, patient defense for disadvantage
33hps
proficiency in STR and Dex
Move 35
No Darkvision
4 Spells (Darkness, Darkvision, Pass Without Trace or Silence)
1 Cantrip (Minor Illusion)
5 ki
No 2nd Wind
No Action Surge
No Damage cantrip
Damage using extra attack and
martial arts (2d8+1d6+12) 24.5
Damage using FOB 32 (2D8+2D6+16)
patent defense, step of the wind,
stunning strike
This is intended to be a melee build so a single class Sorcerer is a difficult comparison and is behind in damage, AC and hp. He can undoubtedly make up for that in spells but that is beyond the scope of what I am looking to do. Compared to a straight monk and a straight fighter, the multiclass keeps up with the fighter in damage (due in part to d10 dex weapons) and is roughly as good defensively while having more spells, better movement, Darkvision but no action surge. Compared to a straight Monk it does less damage and does not have stunning strike but is much better defensively, has more spells, better weapons and darkvision.
Also keep in mind here we are comparing 5th level specifically and while the Monk is substantially outrunning the other three in damage, he would be well behind the triple class in damage at 3rd and 4th level due to fighting style and cantrips.
IME the biggest weakness of the Monk in tier 2 is defense, that is what I am trying to shore up.