Actually you can do a manual color switch by giving each color a different height and pause at each switch layer. Or you can just print each color and glue everything together (in 3mf it's a assembly of different colors you can split them). Or you can print with one AMS printing color only 4 without pink and red and later glue them
Is there a way to print this with only one AMS? It looks like the top-most layers use all 6 colors, so you wouldn't be able to swap filaments to get by with only four.