I don't know but I wouldn't think there was a mechanism for a club to request another is investigated, or accuse another etc.
Our one came about because of the der speigel articles claiming all sorts, and uefa opening an investigation. Which the PL then decided they needed to follow suit.
The Chelsea one came supposedly as a result of self reporting.
Other than that, there would need to be something with some sort of substance in the public domain to make them investigate.
Although 8 clubs did feel they had the right to write a letter to Uefa when our case was in the headlines, so who knows.