Cannot set "Multikey + anything" as shortcut

Could you try manually editing the config file?( ~/.config/hotkeys/synapse.hotkeys)

The multi key is saved as "Multi_key", whereas other modifier keys are saved as "<Ctrl>", "<Alt>" or "<Shift>" (note the parenthesis). As the config file doesn't use any separators between keys ("<Ctrl>space" instead of "<Ctrl> + Space"), it's not possible to use "Multi_key space", as it's registered as one key. Using "<Multi_key>space" results in just space, thus rendering the space key useless. "Multi_keyspace" doesn't work either (of course).

Therefore, I suggest the following:

1.) Use a separator for different keys

and/or

2.) Adress the Multi key by "<Multi_key>" or even "<Super>" (like in Compiz) instead of just "Multi_key"

Since you say compiz maps it to Super, did you try "<Super>space" or whatever Do registers it as?

Ultimately this all is handled in GtkHotkey library, so we won't be able to fix it in Synapse.

Reassigning this to gtkhotkey, since the problem seems not to be in Synapse itself.