Can you do too many strides?

Yes you can. For example, 4000 would be too many.

Do not go over 8

8 is good, but as another poster pointed out 4000 is too many. Other than that, listen to your body and maybe not do them if you feel something hurting you.

I know some like to do the everyday, I'm more of a once a week type but I'm also over 50 and do other speed stuff.

I once did 100 strides.

"Too many" is simply whenever you feel like you're starting to strain or run with bad form, or you're not accomplishing the purpose of what strides are supposed to fill in your training.

Some days that's 4, others 8, maybe even one is too much if your hammy is feeling tender.

For you maybe. 4000 strides is my warmup.

-stay hard