registrations on same pan

Yes.

Provided all the businesses deal in individual goods or services and subject to risks and returns different from those of the other business verticals.

Business vertical is defined u/s 2(18) of CGST Act
Refer Proviso to Sec. 25(2) of CGST Act with Rule 11 of CGST Rules

Yes , you can have registration under vertical Registration.

As per New Ammended Act (31 of 2018) on Dtd. 29/08/2018 , the vertical registration has been abolished , Now taxapyer would able take more then 1 gstn in same state as normal registration ,.... but provision of the Act will come to force only when the council Notifies the same by issuing notification.

Hence at present You can registered yourself under vertical registration