Can I request multiple venues for the same event?

It depends on what you're requesting. For custom requests, yes: you can submit up to 3 requests per event type per date (say, 3 dining requests for the same night), so you've got room to shop around without flooding any one venue with requests.

For pre-bundled packages, plan on requesting just one at a time for the same event. Package bookings charge automatically as soon as a venue confirms, so requesting more than one could mean getting charged for more than one booking if multiple venues confirm.