I think that multiple large parties should be able to host an event at a public park on the same day. Recently I was participating in a volleyball tournament, and there were multiple location switches last minute when the permit was denied because a different party already reserved the park, even though the park has multiple fields. The park was Leroy Haagen Memorial Park.
This caused a great inconvenience to a group of about 300 volleyball participants, who paid to be a part of the tournament. And we had to resort to using Clackamas High School, which was not suited to our needs. In my opinion if there are multiple fields and one of them is not in use, it should still be permitted for large companies to use it.