Have you seen it in summer? Looks as if you have a vine (Virginia creeper?) on the right hand side already and on the netting at the back so you already have 2 green walls to start with.

Thanks! Yes - It gets really green with the vines later on in the season. There are two rose bushes growing up the posts as well. What flowers would you grow on the floor in the partial shade (3-6 hours/day)?

Well, I'm not even gardening on the same continent as you, but in my shady town garden I have a lot of green. There are hellebores, ferns, loads of spring bulbs, pulmonarias, welsh poppies, skimmia ... but it's also important in a tiny space to get the bones right. Ie the hard scape. You already have some walls, steps and beds and it would be good if you could get those nice iron columns properly vertical. I'd lose the rickety trellis and replace with something more robust. I'd also chuck the half barrel. It's clutter. The beds also need to be well cultivated and filled with a good soil mix.

You have several responses to this question on the New England forum, but you haven't returned. Maybe you aren't getting notifications?

https://www.gardenweb.com/discussions/5247259/how-would-you-design-this-brooklyn-backyard?n=6