Ribbon QAT shortcut keys for splitbutton

Using Visual Studio 2008

For a splitbutton on the ribbon (i.e. the main button can execute a command, but also has a dropdown,
for example, the Print button, where clicking does a Print, but it also has a dropdown for Setup, Print Preview, etc.)
When creating a button like that, you can assign different keyboard shortcuts for both the main button and another
shortcut for the dropdown,  i.e. pButtonPrint->SetKeys(_T("p"), _T("w"));

When a button is added to the QAT, however, it is automatically assigned a shortcut, i.e. Alt+1, 2, 3, 4, etc.

The problem is for the split button, only one shortcut is assigned, which causes the dropdown to expand.

Is there a way to have a second QAT shortcut to execute the main command of a splitbutton?