They could make 3 islands with teleport restrictions (1 small only, 1 medium only and 1 large only) and 3 teleports leading in from the main alpha islands. In the middle of the island is a capturable marker or something. When captured a clock starts ticking. A ranking on the main page shows the current holder and time held and the top 10 corps with overall time held.

Holding the marker gives no ingame benefit, just bragging rights. This could evolve into 3 way combat tournaments etc.

Another way to get more pvp is to go the way anarchy online did it in notumwars. Corps can have fields with towers that give ingame advantages in certain places. These towers can be attacked even when placed on alpha. Attacking the towers will flag you for pvp for 1 hour and will allert the corp that their towers are under attack.