I came across 話せる, as the potential form of 話す. However, 話せる can also be found in [dictionaries](https://jisho.org/search/%E8%A9%B1%E3%81%9B%E3%82%8B) as a verb on its own. It can even take inflections, and has its own potential form, 話せられる! I don't really understand what that could mean (*to be able to be able to speak?*).

In [this question](https://japanese.stackexchange.com/questions/5788/whats-the-difference-between-%e8%a9%b1%e3%81%9b%e3%82%8b-and-%e8%a9%b1%e3%81%99/5789#5789), it's presented as merely a form of 話す, along with other potential forms. But there I couldn't find a dictionary entry for 泳げる for example.

How come? Is it just a form that's important enough to have its own dictionary entry, or is it a separate verb? Is it because it has a second meaning (*2. to be understanding; to be sensible​*)?

Are there other verbs like this?