The same way you do anywhere else, since you’re working with the real DOM node as the target of the change event:
handleChange: function(e) {
var options = e.target.options;
var value = [];
for (var i = 0, l = options.length; i < l; i++) {
if (options[i].selected) {
value.push(options[i].value);
}
}
this.props.someCallback(value);
}