Look for clusters of houses while flying above a planet. This is the fastest way I've found to get new multitools. I've found maybe 7 new multitools all better than the last. My newest one has I think 16 slots. Usually when I see 3-4 houses while I'm in my ship I land and search them all. New multitools are in a red box hanging on the wall of the interior of any house. When you approach the red box it will open itself revealing a new gun. These locations don't appear to be marked, that's why I comb the surface in my ship and when I see a pod of homes I stop. Been doing this in 6 systems. Never fails.

Wow nice! Thanks!