Sounds a bit like playing a Star Trek themed game, with all the vastness of the world, but you can only be in Star Fleet.
You pretty much nailed it. Also, this Star Trek comparison is better than X-files as the characters can be posted pretty much everywhere in the empire and also abroad. The author explained this as a way to give a reason for the characters to be together, avoiding the you-met-in-a-tavern clichè. Also, the mood is quite different from X-files, Call of Cthulhu or WFRP, as the PCs are expected to see themselves as the heroes that will save the empire.
There actually are five D&D-ish classes (called cursus - career paths inside the Cohors Auxiliaria Arcana): fighter, explorer, diplomat, scholar (doctor/scientist) and augur ("wizard" doing divination/clairvoyance). Every class is under the protection of a Patron Roman God, for example Mars for fighters.
I figured out the classes are cleverly reskinned D&D ones, with the explorer being a ranger/thief type, the diplomat taking the role of the bard and the scholar that of the cleric (as he can heal wounds through medicine/surgery).
The system is skill-based and there`s no reserved class special power, so for example the fighter can try to do divination if the augur is not available. You throw an exploding dice equal to your skill/attribute value against a difficulty set by the master or against a contrasting roll of the monster/NPC (like in combat). If the PC get the maximum (like 6 on a d6), he reroll and add the result. That's explained in game as the Fate Roll, as the PCs, being members of the Cohors Arcana, are assisted by the Roman Gods themselves.
More or less the rules of Savage World, but a lot simpler.
Furthermore, once per adventure, a PC can ask his patron god to help him, this time only in his expertise field (ie the fighter ask Mars to help him in combat). So the player can reroll the dice and add the result. If a PC displease the gods, the Fate Rolls disappear and he cannot invoke his patron god.
Both the setting and the system are beautiful for one-shots and mini-campaigns, but for a longer campaign...