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Based on the SNES version:
Strength (aka Vigor) is capped at 128 (incl. equipement bonuses) so usually people just leave some buffer there.
Magic (aka MagPwr) is capped at 128 in the status screen but equipment bonuses on top of that do impact the effectiveness of magic attacks.
Again, this is based on the SNES algorithms faq and the research that went into it: https://gamefaqs.gamespot.com/snes/554041-final-fantasy-iii/faqs/13573
110 MAX_LV 99
111 MAX_EXP 15000000
112 MAX_HP 9999
113 MAX_MP 999
115 MAX_STRNGTH 128
116 MAX_VITALITY 128
117 MAX_AGILITY 128
120 MAX_MAGIC 128
122 MAX_ATTACK 255
123 MAX_ABILITY_ATTACK 128
124 MAX_DEFENSE 255
125 MAX_ABILITY_DEFENSE 255
126 MAX_ACCURACY_RATE 255
127 MAX_ACCURACY_RATE_PERCENTAGE 100
128 MAX_EVASION_RATE 255
129 MAX_EVASION_RATE_PERCENTAGE 100
130 MAX_ABILITY_EVASION_RATE 255
131 MAX_ABILITY_EVASION_RATE_PERCENTAGE 100
134 MAX_CRITICAL_RATE 100
135 MAX_CRITICAL_RATE_PERCENTAGE 100
138 MAX_HIT_VALUE 9999
139 MAX_GETAWAY_PROBABILITY_RATE 100
The stats are capped at 128 there, while the damage is capped at 9999. I've tried increasing the damage but 9999 seems to be the hard cap inside the engine as well.