The Mass Effect series did something like it. While in ME1 the classes were not all that different with their powers, things began to change later on in ME2 and especially ME3.
Classes have Combat, Tech and Biotic abilities with the various player classes (and your NPC companions as well) being composed of either a pure class of one type or a mix of two.
The Soldier is purely Combat. Their abilities all have to do with making you better at shooting enemies: with a mix of special ammo that deals better with armored, shielded and unarmored enemies, a guided rocket of sorts that can deal extra damage and a bullet time option that deals more damage and makes you a bit toughter. Their passive abilities make them deal more damage as well and allow them to carry more stuff. In ME3 the more you carry the higher your recharge on your activated abilities is, but because the soldier has only two of them this isn't much of an issue so you can carry a lot of weapons so you can deal effectively with any enemy you are faced with.
The Engineer is pure Tech. They are the debuffer class: their ablities are either a series of fire, ice and lightning blasts that deliver a number of debuffs. They also deploy drones that can mess with enemies at long or short range. They can also hack robotic enemies and turn them against their allies, but those are rare in the game and fought in only a few missions.
The Adept is pure Biotic. They are able to throw around powers that send enemies flying all over the place and can deal some significant damage to tougher ones. They are geared to using their powers often, so carrying light weapons is preferred. This makes them good at breaking hordes of enemies, but you'll need NPC companions to finish them off.
The Infiltrator is a Combat/Tech mix. They have a cloaking power that ups the damage of their first shot when cloaked, allowing you to deal massive damage. This works great with sniper rifles, but also shotguns because your cloaking allows you to sneak up. They have a few powers that make for a good combo (freezing ammo can up the damage of a fire attack), but they tend to have problems with hordes of enemies closing in.
The Vanguard is a Combat/Biotic mix. They are best in closer quarters, and it shows. Their signature powers, Biotic Charge and Nova work together greatly: the first one charges at an opponent and deals massive damage, as well as restoring your shields. The second one drains them completely however, but deals damage in an area around you. By keeping this pattern up you can rapidly deal with a lot of enemies and take all of them down by zipping across the battlefield. However, if something goes wrong and you get surrounded while being unable to pull your attacks off, you're in trouble. Because of the short range they fight in they gain the most from upgrading their melee damage, but this comes at the cost of health so you become even more fragile than you already were.
The Sentinel is a Tech/Biotic mix. Originally they were just the tank that can handle a lot of damage, in ME3 they become a combo character. You see, when a special power hits an enemy that is already under the effect of a compatible power you get an explosion that deals damage to all enemies within range. The Sentinel is geared towards setting up and pulling off as many of these combos as possible, filling the battlefield with fireworks. They also have a powerful armor ability that allows them to take quite a bit of fire, at the cost of a lower recharge on their powers. This means that you have to stay alert and know when to use your armor and when not to, to make sure you have the best damage output possible.
Some of these classes have powers that overlap, but they frequently use them in different contexts. The Engineer might use Overload to deal with the shields of tough enemies, while the Sentinel uses it to set up an explosion.