Is the issue truly that can't you set multiple or that you can't set the background-color?
If I apply your code to the example in the [documentation][1] both styles are added but the background-color isn't used because it is also setting background by default.
google.setOnLoadCallback(drawChart);
function drawChart() {
var data = new google.visualization.DataTable();
data.addColumn('string', 'Name');
data.addColumn('string', 'Manager');
data.addColumn('string', 'ToolTip');
data.addRows([
[{v:'Mike', f:'Mike<div style="color:red; font-style:italic">President</div>'}, '', 'The President'],
[{v:'Jim', f:'Jim<div style="color:red; font-style:italic">Vice President</div>'}, 'Mike', 'VP'],
['Alice', 'Mike', ''],
['Bob', 'Jim', 'Bob Sponge'],
['Carol', 'Bob', '']
]);
data.setRowProperty(0, 'style', 'background-color:red; border: 1px solid green');
var chart = new google.visualization.OrgChart(document.getElementById('chart_div'));
chart.draw(data, {allowHtml:true});
}
<script type="text/javascript" src="https://www.google.com/jsapi?autoload={'modules':[{'name':'visualization','version':'1.1','packages':['orgchart']}]}"></script>
<div id="chart_div""></div>
If you inspect "Mike" the style attribute is incorrectly added. Consider the above example with your line
data.setRowProperty(0, 'style', 'background-color:red; border: 1px solid green');
and compare it to the same thing using this line:
data.setRowProperty(0, 'style', 'background: none; background-color:red; border: 1px solid green');