I have always carried out successional showings with lots of my stuff particularly if they are hybrids.
As a general rule some hybrids were designed to grow within a given time for the benefit of commercial growers so that they can harvest their crop in one go, unlike the amateur gardener who generally wants to harvests over a longer period.
I do not do successive crops of broad beans but I do with French beans, plus I do it with Calabrese & Cauliflower. I am currently picking 2nd crop Calabrese,I picked 3 today and gave one each to my son and daughter and we will have the 3rd.
So the point of my reply is I see no reason why you cannot do this with Broad beans.
I hope you find that food for thought!