configure non-modifier as a modifier key

This question is similar to:

https://askubuntu.com/questions/33751/making-any-key-into-a-modifier-key

I have a machine with a non-standard keyboard layout (lenovo x1 carbon) where the CapsLock key has been replaced by Home, End. I'm used to mapping CapsLock as control, so I used xmodmap to map Home, End to Control:

xmodmap -e 'keycode 110 = Control_L' # Home
xmodmap -e 'keycode 115 = Control_L' # End

When I press Home (or End) alone, the correct keysym is detected:

state 0x0, keycode 110 (keysym 0xffe3, Control_L), same_screen YES,

But I am not able to use the remapped Home or End key as a modifier of any other key: when I press Control+a, the a key is not modified:

KeyPress event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15157752, (829,406), root:(830,407),
    state 0x0, keycode 110 (keysym 0xffe3, Control_L), same_screen YES,
    XKeysymToKeycode returns keycode: 37
    XLookupString gives 0 bytes: 
    XmbLookupString gives 0 bytes: 
    XFilterEvent returns: False

KeyPress event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15157761, (829,406), root:(830,407),
    state 0x0, keycode 38 (keysym 0x61, a), same_screen YES,
    XLookupString gives 1 bytes: (61) "a"
    XmbLookupString gives 1 bytes: (61) "a"
    XFilterEvent returns: False

KeyRelease event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15157912, (829,406), root:(830,407),
    state 0x0, keycode 38 (keysym 0x61, a), same_screen YES,
    XLookupString gives 1 bytes: (61) "a"
    XFilterEvent returns: False

KeyRelease event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15157949, (829,406), root:(830,407),
    state 0x0, keycode 110 (keysym 0xffe3, Control_L), same_screen YES,
    XKeysymToKeycode returns keycode: 37
    XLookupString gives 0 bytes: 
    XFilterEvent returns: False

Whereas if I use a "real" control key, the "a" key press has a control modifier state:

KeyPress event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15160488, (829,406), root:(830,407),
    state 0x0, keycode 37 (keysym 0xffe3, Control_L), same_screen YES,
    XLookupString gives 0 bytes: 
    XmbLookupString gives 0 bytes: 
    XFilterEvent returns: False

KeyPress event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15161477, (829,406), root:(830,407),
    state 0x4, keycode 38 (keysym 0x61, a), same_screen YES,
    XLookupString gives 1 bytes: (01) ""
    XmbLookupString gives 1 bytes: (01) ""
    XFilterEvent returns: False

KeyRelease event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15161588, (829,406), root:(830,407),
    state 0x4, keycode 38 (keysym 0x61, a), same_screen YES,
    XLookupString gives 1 bytes: (01) ""
    XFilterEvent returns: False

KeyRelease event, serial 36, synthetic NO, window 0x1000001,
    root 0xe0, subw 0x0, time 15161842, (829,406), root:(830,407),
    state 0x4, keycode 37 (keysym 0xffe3, Control_L), same_screen YES,
    XLookupString gives 0 bytes: 
    XFilterEvent returns: False

Is it possible to configure the Home key in my case as a Control modifier key? Or is there some hardware limitation that prevents this?