How to map a sequence of keys to <dead_greek>?

I have mapped Insert to Multi_key (also known as Compose) so I can input ä or µ. I've used xmodmap -e 'keycode 118 = Multi_key' in my wm init script.

Now, checking /usr/share/X11/locale/en_US.UTF-8/Compose, I see there are already rules to input Greek letters:

...
<dead_grave> <nobreakspace>           : "̀"   U0300      # COMBINING GRAVE ACCENT
<dead_greek> <A>            : "Α"   U0391    # GREEK CAPITAL LETTER ALPHA
<dead_greek> <a>            : "α"   U03B1    # GREEK SMALL LETTER ALPHA
<dead_greek> <B>            : "Β"   U0392    # GREEK CAPITAL LETTER BETA
<dead_greek> <b>            : "β"   U03B2    # GREEK SMALL LETTER BETA
<dead_greek> <D>            : "Δ"   U0394    # GREEK CAPITAL LETTER DELTA
<dead_greek> <d>            : "δ"   U03B4    # GREEK SMALL LETTER DELTA
...

Problem is, the dead_greek key does not exist in my layout.
I can either use xmodmap -e 'keycode 118 = dead_greek' to map Insert to it, losing Multi key or I can just somehow use the sequence Multi key + g to register as Dead Greek (losing characters like ğ or ġ, which I'm OK about).

How can I do the latter preferably with one line commands to put in my wm init script?

Note that I do not want to mutate /usr/share/X11/locale/en_US.UTF-8/Compose or create a ~/.XCompose and add all the Greek letter definitions again (since they already exist in the system Compose file)

In short, how to Multi_key+g→dead_greek?

update
For a temporary workaround, based on this post, I was able to map shift+Insert to dead_greek. xmodmap -e "keycode 118 shift = Multi_key dead_greek"

Weirdly, none of the modifiers listed via xmodmap -pm are usable here except shift, so this was a compromise…