I looking for annual flowers that proliferate like weeds and produce a steady stream of flowers; preferably in deep saturated reds, blues, and purples.
I plant Zinna's every year which are great for attracting butterflies and bees but I want to add other flowers that last a long time with lots of buds that I don't have to replant every year.
“...I want to add other flowers that last a long time with lots of buds that I don’t have to replant every year. Reds, Blues, Purples...”
You didn’t state your Growing Zone, so you’ll have to see which of these will grow in your Zone.
35 Incredible Red Perennials That Will Never Leave Your Garden Once Planted
https://positivebloom.com/bold-red-perennials-that-will-never-leave-your-garden-once-planted/
30 Captivating Purple-Hued Perennials For Every Garden
https://positivebloom.com/captivating-purple-hued-perennials-for-every-garden-2/
20 Incredible Blue Perennials That Will Make Your Garden Stand Out
https://positivebloom.com/blue-perennials/
Morning glories.