Change your table data using AJAX and then reinitialize your FooTable.

Load more data via ajax

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Refresh After Populating By Ajax

You can easily tell Footable to redraw by triggering the footable_redraw event on the table:

$('.get_data').click(function() {
	$.ajax({
		url : '/some/api',
		success : function(data) {
			$('table tbody').append(data).trigger('footable_redraw');
		}
	});
});