You can't modify a built-in group. Instead, hide the group, then reconstruct it from iDMso commands, including your custom button. Here's some sample XML that show how to replace a group:
<contextualTabs>
<tabSet idMso="TabSetChartTools">
<tab idMso="TabChartToolsDesignNew">
<group idMso="GroupChartType" visible="false"/>
<!-- Add new Chart Type group -->
<group id="ReplaceChartType" label="Type" insertAfterMso="GroupChartData">
<button
id="ChartChangeCustom"
size="large"
imageMso="ChartInsert"
label="Change Chart Type"
supertip="Change to a different type of chart."
showImage="true"
showLabel="true"
onAction="ChartChange"/>
<button
id="ChartImproveLegend"
tag="LegendButton"
getEnabled="GetEnabledMacro"
size="large"
imageMso="ChartPrimaryHorizontalAxisTitle"
label="Improve Legend"
supertip="Improve legend on some chart types."
showImage="true"
showLabel="true"
onAction="ImprovedLegend"/>
</group>
</tab>
</tabSet>
</contextualTabs>