I can easily mix up any ingredients in my cement mixer compost sifter. I can't get inexpensive vermiculite in the large 3 cubic foot bags anymore, so the head guy at our local nursery suggested I just mix a good quality topsoil with my chicken run compost 1:1. All I do is toss in a couple shovels full of topsoil, then a couple shovels full of chicken run compost. The sifted material drops down into my Gorilla cart in thin layers, essentially mixed. That is my "magic mix" for my raised garden beds.
I also have different sized screens I can put in the compost sifter barrel. I have a 1/4 inch mesh for making potting soil mixes, a 1/2 inch mesh for topping off the raised garden beds, and without a screen insert, the 1/2 X 1 inch mesh on the barrel itself is good enough for top mulch. I suppose I would not have to sift the top mulch, but it's so easy for me to sift compost with my cement mixer compost sifter that I prefer to sift out the material and toss the rejected bigger material that is not yet composted back into the chicken run for some more time to break down.
I tried sifting out some chicken run compost with the 1/4 inch screen for potting soil with my seed starts in the house. That was a mistake. The chicken run compost is full of life and I had all kinds of little flies and bugs in no time with those seed starts. Probably not a problem if you started seeds in that chicken run compost potting mix outside in a greenhouse, but it was not good for inside the house due to all the bugs.
Lesson learned. This year I purchased sterile potting soil from the store and did not have any bug problems with my seed starts. I hear you can bake compost to kill all the bugs and eggs in the compost, but I don't know if all that work is worth the time and effort for me.

Also, and I don't know anything about this, but I wonder if killing all the life in the compost to use it as potting soil really defeats the purpose of using compost in the first place?