Can a Ranger, at some point in it's career, take both Archery style and Two-handed style class features in order to broaden their efficacy? Can a Rogue take both Artful Dodger and Cunning Sneak or Brutal Scoundrel? If so, when and how is this done?
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In general, the answer is no.
In practice, the answer is...sort of, but not really, and definitely not as well. If it's possible it will be via feats and/or paragon paths.
For the specific cases you've mentioned:
With the methods I've listed above you won't qualify for the riders, but with the epic feat you will.
4e classes are designed for the most part to be pretty compartmentalized and dipping into other class features is in general not supported. There are some cases where it's possible (especially in cases where the feature provides a bonus feat or something that can be replicated with a feat), but they are going to be epic level feats and by that time you may not have the flexibility to properly utilize them.
So the long and short is that you can rarely just grab another class feature, but more often you can replicate the functionality.