Draw a menu (not popup menu) in any rectangular region of a window with MFC

You can't change the size of a normal Windows-drawn caption bar. That's determined by the user settings and the theme. If you're drawing things yourself, then you also define the caption dimensions yourself. You can paint whatever you want wherever you want, so you can paint your caption bar over what would normally be considered the client area. To make that extra region behave as though it's really the caption bar, handle the wm_NCHitTest message and return htCaption.

Note that GetSystemMetrics does not accept a window handle as one of its parameters. That means that it cannot return window-specific metrics. As its name suggests, it gives you system-wide metrics.

Simple answer: No. Not for a specific window.

Complicated answer: The border is drawn as part of the "non-client" region of the window. This is all handled (under the hood) by the default processing (i.e. DefWindowProc), along with the caption, minimize, maximize buttons, etc. You can override this by handling the WM_NCPAINT message. You'll then be responsible for drawing the entire non-client area of your window. You'll also want to handle the WM_NCCALCSIZE message, so that Windows knows how much of the remaining space to give to your client area.

Alternatively, you can set the border style of your window to none. This will allow Windows to draw the caption for you, although it'll probably look slightly different. Unfortunately, by doing this, you lose the drag-to-resize functionality. For that, you'll need to handle the WM_NCHITTEST message.