I had this question myself and found an answer eventually (thanks to this reddit post)

There is a rather simple way to extend the compose key.

You simply have to create the file ~/.XCompose and put your new key combinations in there.

Example of my XCompose file:

> cat .XCompose 
include "%L"

# Math symbols
<Multi_key> <p> <i>                 : "π"   U03C0    # GREEK SMALL LETTER PI
<Multi_key> <S> <i> <g>             : "∑"   U2211  # Sigma


# Misc symbols
<Multi_key> <asterisk> <asterisk>   : "•"   U2022  # bullet point


# Agda symbols
<Multi_key> <T> <o> <p>             : "⊤"   U22A4  # Down Tack/Top
<Multi_key> <B> <o> <t>             : "⊥"   U22A5  # Up Tack/Bot

> …

You just need to add them in there, I use This Site to find the UNICODE value of the character, in case anyone wants a site, though there are many alternative ways to find it.