Three possible ways:
A) Like Robert M. said, if they all go through a couple of busses, tune the volume on the bus(sses)
B) Regroup all those object under a hierachy of Actor-Mixer, and change the volume of the Actor-Mixer. This adds a volume offset to the children. The Actor-Mixer purpose is to share some properties with a group of objects.
C) Multi-select all your 1000 objects in the Project Explorer, right-click and select Multi-Edit. Expand the "Audio" node and enter 6+ in the Volume box (means "add 6"). If you enter only 6, it will set 6 to everything, which is not what you want.
There is no volume limiting feature in any of those scenario. But you could do a Query (F3) to gather all objects that are over 0dB in volume and set them directly.