Possible workarounds from StackOverflow:
https://stackoverflow.com/questions/35939222/single-series-drilldown-to-multiple-series-highcharts
https://stackoverflow.com/questions/36354584/highcharts-multiple-series-drilldown-to-multiple-series

<script src="https://code.jquery.com/jquery-1.10.2.js"></script>
<script src="http://github.highcharts.com/highcharts.js"></script>
<script src="http://github.highcharts.com/modules/drilldown.js"></script>

<div id="container" style="min-width: 310px; height: 400px; margin: 0 auto"></div>
<script>
$(function () {

// Create the chart
// type to line for line chart
$('#container').highcharts({
chart: {
type: 'column'
},
title: {
text: 'Basic drilldown'
},
xAxis: {
type: 'category'
},

legend: {
enabled: true
},

plotOptions: {
series: {
borderWidth: 0,
dataLabels: {
enabled: true,
style: {
color: 'white',
textShadow: '0 0 2px black, 0 0 2px black'
}
},
stacking: 'normal'
}
},

series: [{
name: 'Things',
data: [{

name: 'Animals',
y: 5,
drilldown: 'animals'
}, {
name: 'Fruits',
y: 2,
drilldown: 'fruits'
}, {
name: 'Cars',
y: 4,
drilldown: 'cars'
}]
}, {
name: 'Things3',
stack: 1,
type: 'line',
data: [{
name: 'Animals',
y: 8,
drilldown: 'animals3'
}, {
name: 'Fruits',
y: 7,
drilldown: 'fruits3'
}, {
name: 'Cars',
y: 10,
drilldown: 'cars3'
}]
}],
drilldown: {
activeDataLabelStyle: {
color: 'white',
textShadow: '0 0 2px black, 0 0 2px black'
},
series: [{
id: 'animals',
name: 'Animals',
data: [
['Cats', 4],
['Dogs', 2],
['Cows', 1],
['Sheep', 2],
['Pigs', 1]
]
}, {
id: 'fruits',
name: 'Fruits',
data: [
['Apples', 4],
['Oranges', 2]
]
}, {
id: 'cars',
name: 'Cars',
data: [
['Toyota', 4],
['Opel', 2],
['Volkswagen', 2]
]
},{
id: 'animals3',
name: 'Animals3',
type: 'line',
stack: 1,
data: [
['Cats', 2],
['Dogs', 3],
['Cows', 1],
['Sheep', 1],
['Pigs', 1]
]
}, {
id: 'fruits3',
name: 'Fruits3',
type: 'line',
stack: 1,
data: [
['Apples', 4],
['Oranges', 3]
]
}, {
id: 'cars3',
name: 'Cars3',
type: 'line',
stack: 1,
data: [
['Toyota', 4],
['Opel', 3],
['Volkswagen', 3]
]
}]
}
})
});
</script>

This would be great. Right now we do a hack to generate our own drilldown but this means we lose the drillUp ability. Integrating this directly in the drilldown function built into highcharts is a more ideal solution (with drilldown, xAxis label clicking, and drillUp).