The Calcite dropdown component has a close-on-select-disabled property that allows the dropdown to stay open even after the user changes the selection. This is especially useful when selection-mode is set to multiple, as it allows the user to select multiple items without having to reopen the dropdown after every selection.
I would like the same functionality in the split-button component, which I prefer over the dropdown, because the secondary button is a nice visual indicator that there is hidden content (dropdown-group(s) with dropdown-items) that can be revealed with a click.