Love the Tuscan Olive color for the stucco and my vote is yes to matching the stairs to the trim. A third color as a pop would be a great way to add dimension and there's a lot of different ways you can go with it. You can go punchy and fun or subtle but strong contrast. I personally like the chestnut or clay color with the olive for strong yet not loud contrast, a rich plum for deep contrast (couldn't find a picture with a plum example.)

You could also consider stripping the stairs and trim to a polished natural wood that gives a great contemporary look and feel:

I strongly recommend you do not replace the vinyl with more vinyl. It is not a good idea for moisture reasons. Concrete or even wood siding is best.

The third color on your home could be the window grids, maybe? I think you are right on with the olive.

Yes to olive. I would do ceder where vinyl is.