Absolutely; and each player might have a different idea of what a class' "role" is in combat, even side by side at the same table!
An example: some people I game with like to play what I call "light" Rangers; light-to-no armour scout and archer types that try to give out damage without taking any - I think those are called Strikers. But then there's me; if I'm playing a Ranger it's going to be "heavy": I'm going to put it in plate mail and tank it up, as Rangers - particularly in 1e - are usually pretty tough and in my view should be throwing their hit-point-laden bodies into the fray to defend the squishies - which makes them Defenders.
Clerics are another good example of a multi-role class.
Lan-"I'm not sure this is what they meant when they said it was a role-playing game"-efan
But there's a good example. If you're playing a "tank" ranger, then why play a fighter? The ranger has more hit points, better special abilities, all sorts of other goodies, although a slight xp hit. So, what's the point of having the fighter class?
Well, I suppose you could argue that because the of the stat requirements, you need a fighter because rangers were harder to qualify for, but, that seems kind of lame. "We have fighters for those who just aren't good enough to be rangers"? Yay, an "also ran" class.
And, funnily enough, people talk about classes doing multiple roles. Yet, it's almost always the casters - I want to be a defender/striker/whatever wizard, goes the refrain. Yet, I rarely see it go the other way.
Do you want the thief/rogue to be able to create area of effect effects and lots of buff/debuffing like a controller? How about the ranger? Should rangers be able to create area effects? Maybe he's just shooting a cloud of arrows wuxia style which burst into flame and create fireballs. Or, maybe the rogue should be healing people and giving them extra actions per round a la a leader. After all, I can think of all sorts of rogue leader archetypes... or well... maybe not.
Somehow I don't think too many people want that in their core rules. Niche protection for a class means that a given class actually has a reason to exist. If any class can cover any niche, why bother having classes in the first place? Go GURPS or HERO and be done with it.