Further Information & Links
No, not if you have "only" a Master's degree in Advanced Studies.
See regulations dated December 16, 2010: "Weiterbildungsabschlüsse der Stufe Master of Advanced Studies berechtigen nicht zur Zulassung zur Promotion"
You can discuss with your supervisor, whether you can take PhD courses at other universities in order to fulfill the requirements min. 9 KP in Modul I (methodological courses).
You will find all of your professors and their research areas at https://wwz.unibas.ch/en/people-and-areas/
Please contact them directly.