Once a high value open competition bid is open and two quotations are received, is it fair to call another quotation to make three quotations or not?

Well, its totally unhealthy. Anyway, you have2 options1. Is to extend the closing date of tender submission. BUT, all received tender should be unopend till receiving some addional offers.2. Is to have a permission from your tender committe to open the available tenders. But once its opened its totally unfair to ask for new ones.

What about transparency if bid value is quite high and most of competitors know what is the market scenario?

getting3 quotation at less for each order is the right way to market analysis ,