Can I chase several premium names at the same time?

Yes — the dedicated server provides multi-core capacity to run many non-blocking EPP sockets in parallel, which is exactly what pursuing several names at once requires.

A couple of things to keep in mind:

• Concentrating on a single premium name (single-mode) uses the most resource per catch, so if you spread across many simultaneous releases, plan your list against the server's capacity.
• The heavier the contention on each name, the more of the server's parallel capacity that name will want.

The dedicated tier exists so you are not rationing capacity against other users — but it is still finite, so prioritise your highest-value targets when several premium drops coincide.