Nope. Once you set up your department, that carousel is gone for good.


Short of fate-locked pets at the Labyrinth, Betraying the truth about the Murderer to stay put, an 5-turn option on a rare card drawn (if ever) at the Side Streets Look closer, when finished with the University end option for Solving cases Around London, Return the squeezebox for some glim, one one-time very esoterically offered at the time Ambition: Heart's Desire - the Topsy King 7 if you have that Ambition The Correspondence?, the seasonal examining pails of so called snow with your monocle (you have a 70% success rate at 7 and lacre taste caps at 6,) the (if one already) Correspondents' seasonal 15 SoTC broad check with Snow and lastly,
Something Perilous Bundles likely from Surprise packages
offer raising this up to 10.



Only the regular University option and Court (if not kicked out) are left. More on the latter below.


However, that earlier option you are asking about is a 50/50 luck check with severe penalties for failure. Even if you had access before, it's best you build up Persuasive and grind Somewhat challenging music Symphonies at the Court (using Indulge yourself with the lead if you can get a high rate or surefire victory. My Author and future Correspondent with 167+ Persuasive gets 15 Inspired per turn this way, and can grind one work out around her 20 turn cycle, give or take any crads I want to play/entry into Court.)

I guess if you still have University access, if you ground out the University Connections with their Endowment of a University Fellowship and Church's Tiny Jewelled Reliquary connection items, you could afford mining it.
But honestly, the turns needed to get to that Term Passing 12 would just be better spent making Symphonies. (Just don't get kicked out of court until you are done with that.)