Can a person obtain another gstn number?

Sec -25(1)and (2) of CGST Act,2017 clearly state the law. 

Yes, it is possible to obtain another GSTIN with a different company name in the same state, having a different line of business as GST Registration is PAN based and State specific registration. Every business has distinct PAN number which can be used to obtain GST registration in same state in case of different business activity.