How does a solo professor use multiple spells?
Professors get benefits when they have multiple enhancements, or when their foes have multiple impairments.
For enhancements, I know of the base protection charm (3 focus), the proficiency charm (7 focus), and brain elixir (30 minute potion).
For impairments, I only know of the deterioration hex.
What else counts?
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The deterioration hex is the only impairment a professor has. To get others you need to team up with an auror.
For enhancements you can also have a trace tonic active, and if you use a dawdle draught and still have casts left over that will also count as an enhancement in the fortress.
Dwaddle counts?
... HOLY BLEEP, that makes that potion so much more valuable.
... Oh, none of the skills are "x power per enhancement"? They max out at 2 enhancements?
Dwaddle: 6 hours, and if attacks don't count as attacks, lasts for all your combats.
Trace Detection: 7 hours cost, 30 minutes use
Brain: 12 hours cost, 30 minutes use
Hmm, looks like I knew of the worst of the 3 :-)