In case people are wondering the maxes for item specialists, of course gotten from GameFAQs:
(Note: These maximums are per character, not item; Having 2 300 Statisticians on two different items equipped on one character is a waste of 300 Statisticians -_-)
Statistician - Increases Exp. gained from enemies - Caps = 300
Broker - Increases HL gained from enemies - Caps = 300
Manager - Increases Mana gained from enemies - Caps = 300
Armsmaster - Increases Weapon Mastery rate - Caps = 1900
Dietician - Increases HP - Caps = None
Master - Increases SP - Caps = None
Gladiator - Increases ATK - Caps = None
Sentry - Increases DEF - Caps = None
Teacher - Increases INT - Caps = None
Physician - Increases RES - Caps = None
Marksman - Increases HIT - Caps = None
Coach - Increases SPD - Caps = None
(Note that the apparent max for any one stat on a character is ~21.4 million, according to HolyLancer9)
Firefighter - Raises Fire Resistance - Caps = 90% Resistance
Aeronaut - Raises Wind Resistance - Caps = 90% Resistance
Cryophile - Raises Ice Resistance - Caps = 90% Resistance
Alchemist - Adds chance of Poison to attacks - Caps =100
Hypnotist - Adds chance of Sleep to attacks - Caps =100
Witch Doctor - Adds chance of Paralyze to attacks - Caps =100
Gangster - Adds chance of Deprave to attacks - Caps =100
Amnesiac - Adds chance of Forget to attacks - Caps =100
Pharmacist - Increases Poison resistance - Caps = 998
Coffee Maker - Increases Sleep resistance - Caps = 998
Social Worker - Increases Paralyze resistance*- Caps = 998
Medicine Man - Increases Deprave resistance* - Caps = 998
Psychologist - Increases Forget resistance - Caps = 998