Ok, here are some suggestions. Not all of these will be easily bought at garden nurseries, but they might show up. Also, I know these are native to Massachusetts, but I’m not certain they are all native to Rhode Island.
These prefer slightly damp sites, but they will probably do fine in shade with some mulching:
Northern Maidenhair Fern, Adiantum pedatum
Wild Ginger, Asarum canadense
Jack-in-the-Pulpit, Arisaema triphyllum
Bellworts, Uvularia grandiflora, U. perfoliata, U. sessisilifolia
Canada Lily, Lilium canadense
Cucumber Root, Medeola virginiana
Trilliums, T. cernuum, T. erectum, T. undulatum
Canada Mayflower, Maianthemum canadense
Solomon’s Plume, M. racemosum
American Spikenard, Aralia racemosa
Golden Alexanders, Zizia aurea (Z. aptera might be native in RI also?)
White Wood Aster, Eurybia divaricata
Blue Cohoshes, Caulophyllum giganteum, C. thalictroides
Cardinal Flower, Lobelia cardinalis - this is likely to be short-lived, but it is glorious when it flowers
Wild Geranium, Geranium maculatum
Squirrel-corn and Dutchman’s-breeches, Dicentra canadensis and cucullaria
Bloodroot, Sanguinaria canadensis
Baneberries, Actaea pachypoda, A. rubra
Wild Columbine, Aquilegia canadensis - likely to be short-lived, but sometimes it re-seeds itself
Foamflower, Tiarella cordifolia
These generally prefer more sun and can take drier soils:
Wood Lily, Lilium philadelphicum
Switch Grass, Panicum virgatum
Little Bluestem, Schizachyrium scoparium
Indian Grass, Sorghastrum nutans
Butterflyweed, Asclepias tuberosa
Eutrochium spp. - these prefer damp soils, but drier soils will keep them from taking over the garden (maybe)
Northern Bush Honeysuckle, Diervilla lonicera
Wild Indigo, Baptisia tinctoria
Wild Senna, Senna hebecarpa - I think this prefers dampish soil, but it should do fine in “ordinary garden soil”
Mountain Mints, Pycnanthemum incanum. P. muticum, P. tenuifolium, P. verticillatum, P. virginianum - spectacular for attracting pollinators
Sweet-fern, Comptonia peregrina - this will likely spread a good bit if it’s happy
American Pokeweed, Phytolacca americana - big, messy, and spectacular
Virgin’s Bower, Clematis virginiana - prefers dampish soil, but happy enough if it’s not too dry
New Jersey Tea, Ceanothus americanus - great for attracting pollinators
Various other asters and goldenrods would also be good, but I don’t know enough to say which ones would do better in a sunnier/drier site versus a shadier/damper site. E. divaricata spreads itself around in my garden in dry shade; Symphyotrichum cordifolium does well in a somewhat sunnier and damper site. S. laeve is a beautiful and well-behaved aster in my garden. New England and New York Asters are always worth trying.
I’ll leave you with advice from my mother: Keep planting things until something does well; then plant more of that.