This is the thing though... You CAN, but why would you? Yes, you can go pure Mage, but there's nothing in it for you. You can be just a gunslinger, but there's no benefit for you.
This is how I'd like to see it work. Have your character on a triangle scale. Skill, Will, Strength. Each point favours certain weapon types and advancing in areas, or multiple areas, unlocks single skills or cross-class skills. Go full on brute warrior? Well, you're obviously good with a great big sword, but keep going, and you hold it better, swing better combo's. Once you hit specialization, you have Sparta style kicks that can shove enemies, or knock them across a room. If you go pure Skill though, you gain Skill specific advantages.
But say you go for both... you're moves become flashier, quicker, you're lighter on your feet, gain better dodging skills and can disarm and counter, pistol whip and pull flashy from-the-hip shots.
That's just one cross-class. And it doesn't have to stop there. Keep advancing in a certain weapon type, or shift you balance a little, and you get more specific skills, and even disadvantages. Maybe if your mostly Strength and start to up your Will, getting hit too often will spark some magical rage mode that will sap your health but won't stop until you've killed everyone, even innocents, and each kill gives you a little more time... fight against your nature, so as not to slaughter innocents? Good luck doing much magic later on then... you need to struggle to regain your powers.
This is just the tip of the iceberg. Imagine all the different things you could do with this character generation, when you take into account all the balances you can strike, the benefits and risks of moving up and down in one, the weapon specializations coming into it, your Good/Evil alignment... this is how I always pictured Fable.