if you don't specify any colours when creating a chart or adding a series, highcharts will pick one from it's default colours. there are a limited number of defaults.

however, you can tell highcharts about a new set of default colours, so you could give it more to chose from, up to the maxumum you want to support. this code sets 9 defaults, but you can add as many as you want, you just need to come up with some unique colours:

     '#058dc7', '#50b432', '#ed561b', '#dddf00', '#24cbe5', '#64e572', '#ff9655', '#fff263', '#6af9c4']

make this the first thing you call.

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