(4 Player) Can the Trogs build their Tunnels anywhere? (I'd assume yes). Except for HQs. And with the understanding that there would be no point building one where one already exists.
A Trog Tunnel (according to Rules as Written) can only be placed in a Region that the Trogs control.
Rulebook, pg 9 wrote:
• Structures cannot be Built in a Region with a Battle token.
• Structures cannot be Built in a Headquarters Region.
• Multiple Structures of the same type cannot be Built in a single Region.
• Structures in a Battle Region cannot be Activated, unless explicitly stated by a card.
• If a player loses Control of a Region with their Structure, the Structure remains, but the owning player cannot Activate it (unless a card indicates otherwise), until they regain Control of the Region.
There are no rules in Playing the Trogs, Clarifications, or the Official FAQ that would break the general structure rules for the Trog's Tunnel structure.