Yes, If you wish to take admission to private BAMS college in Pune,

Firstly I like to mention that in BAMS course you have to study yourself with the guidance of seniors and professors. So from my point of view it doesn't matter where you take admission.

But still also I'll gives you list of BAMS private colleges in Pune.

• College Of Ayurved And Research Centre, Akurdi, Pune
• Dr. D. Y. Patil College of Ayurved and Research Centre, Pimpri, Pune.
• Bharati Vidyapeeth's Ayurved Mahavidyalaya, Pune
• Sumatibhai Shah Ayurved Mahavidyalaya, Pune
• BSDT's Ayurved Mahavidyalaya, Wagholi, Pune

Below mentioned is the link where you can find more details about the colleges,

https://medicine.careers360.com/colleges/list-of-bams-colleges-in-pune

I hope you might find this answer helpful.