You need a zone and nearest city. I don't understand why your maple tree doesn't provide the shade you want, but you think a different tree would.

PDX = Portland, OR so likely a zone 8. Maple is probably a Japanese maple, which are not known for great shade production due to size. Crabs are a possibility but also pretty small. I'd consider a magnolia, Acer griseum (paperbark maple), sourwood, Persian ironwood (Parrotia) or a Stewartia. Afternoon sun likely too strong a position for a dogwood in this climate.

Portland, Oregon it is.

We’ve really appreciated the shade this plain old maple tree provides during the summer, especially how it blocks the afternoon sun from coming through the door and helps keep the patio cool and shaded. I planted it back in 2004, not knowing much about trees at the time. Lately, I’ve been reading about the potential risks of maple roots damaging foundations, which is the only reason I’m considering removing it. The area doesn't get any morning sun—just afternoon and evening sun.

That IS a Japanese maple. Unlike some of their cousins, they do not produce an aggressive root system and are often planted in close proximity to structures for that reason.

You really do not have much reason to worry. Unless the house foundation is already cracked or damaged/compromised, tree roots are unlikely to cause any damage.

Thank you!! That is great to know . What a relief. No damage noticed so far anywhere.