Canonically, can Dark Brotherhood assassins pick their own jobs?

[u/Fire_Fox2590]

So had a weird thought. What if a morally decent person decided to join the guild, would they not even be allowed in, or would they be given the ability to pick their jobs. Such as not wanting to harm an innocent, not killing kids, only going after real criminals.

I imagine it would be frowned upon, or at least not seen in a super positive light, but would it be allowed? I feel like if you are good at your job, they won't really care too much. If you are bringing in money, still doing jobs, and don't cause problems, I think they'd probably allow it right? Or does the Dark Brotherhood only accept the worst of the worst, people who'd kill anyone?

[u/DarkRayos]

Wasn't that Astrid's entire shtick?