invoice - reg

Yes it can be possible you need registeration in every state and copy of invoice to all the the three places should be send.

in GST a registered dealer can sales his goods to any where. There is no resitricitoin on sales.

In GST, there is only two column:

First for buyer and second for the delivery place.

So if consignee is your buyer then mention Tamilnadu as buyer and Kerala as delivery place.