I used to play the cajon a lot with brushes, this way I could get a hi-hat, kick and snare sound. When hitting the snare and kick sounds while holding brushes you have to hit with the stick part of the brush to get a fuller sound especially when playing without mic. And the hi-hat sound comes natural from the brushes hitting the box.
Without brushes I find it harder, I've seen people screw one of the top corner sides loose so that you get a different snare sound on one side, more like a rimshot, I have used this but never really stuck with. It also really depends on the string inside the box how this will work out for you, might just have to try it.
Another thing you can do with the sound is put one foot against the front and push against the box and slowly release pressure, this pitches the sound of the entire cajon, would experiment with this to see how it feels / works for you personally.
That being said, the cajon has its roots with people who had to invent instruments which they could disguise cause they were not allowed to play music. I would imagine it took them quite some experimenting and creativity to find/create this instrument. Don't think there is a right or wrong way with a cajon if it sounds good.