I am sure we can enter as many as we want, have entered several on the 12 days of Christmas thingy. I think there is a tech glitch this morning, have tried to use the search button and just get an error message.
Yes always a good idea to raise any site issues in site stuff as then we will definitely see them. You are right about only being able to enter one competition once. Also about the search issue which I believe began yesterday and is currently being worked on by tech.
But absolutely - you can enter as many comps as you like - do let us know which one was causing problems and we can investigate