"First possibility: Shenghe sweetens the deal by tipping in more money." - Unlikely, would only happen if they see a "No" vote possible.
"Second possibility: another company makes a counter offer." - Highly unlikely, Shenghe has a stranglehold on PEK through their almost 20% holding and the 100% take-off agreement. (Wished I was wrong, though, never liked that take-off.)
"Third possibility: the deal falls through, Shenghe walks away, and Peak has to go it alone." - Also unlikely, walking away is not in their or the CCP's rule book, especially in the REE space (see the NTU saga for instance).
"If Peak has to go it alone, the risk is massive, and you’ll see the share price tank, at least in the short term (depending on how well the company manages to execute.)" - Yes, I agree with that scenario but won't happen, see above.
Expand
(20min delay)