Yes, it is possible and may be common as well (I don't think there's enough data on this).

There shouldn't be any issue with claims as such if all your disclosures are correct and while taking the second, third or the next policies, you've clearly declared about your existing policies.

Although, having multiple policies especially from different companies would mean a little more work for you (remembering to pay the premium, updating any details like contact details, address, nominee) and for your nominees (intimating claims to different companies, filling out multiple claim forms and the follow up, if required). So, yes, the claim process may be a little tedious and complicated. But with IRDA/Govt coming up with the eIA account and dematerialisation of insurance policies, some of these hassles may be solved.

Thank you