For the purposes of this question, we're going to ignore the rules, found in either the Player's Handbook (pg. 187) or Xanathar's Guide to Everything (pg. 134), that allow a character to learn a tool proficiency as part of their adventure downtime. For our purposes, we assume that these methods of gaining tool proficiencies are not available to us.
So given that constraint and the constraints below, what is the maximum quantity of tool proficiencies a character can learn as part of their normal progression?
- Only officially published 5th Edition sourcebooks
- No Unearthed Arcana,
however tempting it might be to include the newly released Artificer revisionthere is an officially released version of the Artificer, and that is valid.
- Temporary effects, i.e. tool proficiencies gained from from spells should only be included if the character in question is capable of applying/maintaining said effects themselves.
- No proficiencies gained from magic items
- No use of downtime activities to learn new proficiencies (PHB pg. 187 or Xanathar's pg. 134)