Taskbar won't show more than two buttons

If I open two programs/windows, both buttons will appear in the taskbar.
If I open more than that, only two will appear in the taskbar but a pair
of scrolling arrows appear just to the left of the Notification Area
(system tray). I can use either arrow to scroll a desired program onto
the taskbar, then click the button to open its window.

If I select the Show Windows Side by Side, Stacked or Cascaded, all
windows open as selected, but in the taskbar no more than two buttons
appear.

Very annoying. I do not have the Group Similar Taskbar Buttons option
selected.

Thanks for your suggestions.

R1