yes you can have all the genes in one snake. the quickest way to get 4 in a snake....

breed 2 morphs together, you make double hets
also breed the other 2 morphs. you make double hets of them.

breed the double hets from one pair of morphs and hit the 1/16 odds of a double recessive, then do the same for the other pair of morphs and also hit the 1/16 odds.

then breed the two double recessive together. making quad hets.

breed the quad hets together and hit the 1/256 odds and theres your 4 recessive in one snake.