In general, no. First of all, definitely don't send them to original (old or cutting edge) literature. It's just too hard. But really sending them to advanced textbooks is too tricky also. Kids in Algebra 2 need to learn that stuff first, not Artin.
Second, when I say "in general", probably the majority of your kids don't have A/A+ level capability in what they are doing now. Throwing more on them is not kind, in that case.
I do think there is a way to do enrichment. But it's maybe a bit more of a tease. "If you ever take abstract algebra, they'll show you why quintic general solution doesn't exist." I say this as someone who had it explained to me thus. AND who still has only this level of understanding. (I've never taken abstract algebra, so that's my level of understanding of it.)
For the sharper, more curious kids, you can maybe direct them to contests. It won't just be the problems then, but some interaction with other kids in an after class setting. Also Numberphile or Mathologer videos are good stuff. Or the Andrew Wiles video (ripped copy has been up on Vimeo for years). There are some good books also, in particular Flatland.
Avoid any push for doing original research. It's just not feasible for high school kids in math. If you have to, just do some statistics things or descriptives (like the thread we had on pictures/sculptures of shapes). I.e. take a "big tent" view of what passes for math. Your administrators won't know the difference and will probably think you are complying. (Maybe even you are, if you think a little sideways.)