How can I make a bright, multi-colored rug work in my living room?

Sounds perfect! You have a bunch of neutrals going on, that will add a pop of color. Then once the rug is chosen, pick bright colors out of the rug to be used for accessories - lamp, throw, pillow, photo frames, vase, etc.

Sounds like it will work just fine & help break up the monotone from your walls & furniture. Adding pillows,candles,vases,pictures, pieces in & around room that have the same pops of color from rug will tie it all together. Mix the colors don't stick with just certain one from rug. Just don't get carried away with it or it could look too busy and get stressful.One or two of several of the colors evenly spaced around room the, colors that you love, It'll be beautiful. Here's some pics/ideashttps://www.perigold.com/rugs/pdp/companyc-captiva-green-red-area-rug-jxx1565.html MORE https://www.overstock.com/Home-Garden/Area-Rugs/31446/subcat.html?featuredproduct=9509480&featuredoption=14112826&kid=9553000357392&track=pspla&ci_src=17588969&ci_sku=16688682-000-000&cnc=US&cid=248963&type=pla&targetid=pla-538765374880&ds_rl=1263867&gclid=EAIaIQobChMI-7zcr8LP3wIVpiCtBh0IYAfhEAQYBSABEgKZjPD_BwE&gclsrc=aw.ds MORE https://www.pinterest.com/pin/59109813844400139/visual-search/?x=11&y=11&w=352&h=446 Rules??? if there really are any https://www.apartmenttherapy.com/the-key-to-color-confidence-may-just-be-the-60-30-10-rule-249257 Just remember most of all it's your home & you'll be living in it so enjoy the great colorful bright cheerful rug

Sounds to me it should work just fine. Balancing the color and brightness of the rug with everything else in the room with off-whites and whites will keep everything in check.

throw pillows with the color of the rug maybe a throw on the back of a chair with the colors in it put around some vases in the colors of the rug