#Destiny2 Little Tips: Synthweave (for transmog) caps out at 15 per guardian.
The game does tell you this if you hover over their icons in the appearance customization screen, but it's kinda of hidden.
If you're spending this downtime to score some fashion, make sure you actually unlock some ornaments before reaching that cap. I'm pretty sure they don't stack anywhere else, they just get burned. Like I'm pretty sure I did a while ago.
