I may have misunderstood your question, but …..
to find relatives, or matches, distant or otherwise, wouldn’t you be presented with these in your DNA results with whichever company you tested with?
Wouldn’t you then contact those people to try to work out how you connect, if you don’t already know?
Could you also suggest that they download their raw data from their testing company to gedmatch?
If any relatives are already on Gedmatch, can’t you see who you match with? I don’t really use Gedmatch much so am not too familiar with it, but I thought it was a site where people who have tested with any dna company can put their data and find matches?
In addition, depending on which company you tested with, you can also upload your raw data to other companies in the hope of getting more matches that way. There is a fee to unlock all the features of the sites though.
OR.
Are you looking to expand your paper trail with information such as that supplied by LH?