No, currently the only way to get more fragments is by increasing mission level. Fragments drop increase as the mission level goes up and are capped at 700% gain at +10 level. Boost items (like tarot cards or meme virus) have no role in the tech fragment drops.

Here is @MARCOPOLOCS‍ ' clarification.

Don't get me wrong, TA is a fun class and in my view closest to the inquisitor as it should play (a fragile guy directing his retinue, as opposed to e.g. the crusader who gives the space marines a run for their money). But once you get to the weapon levels 90+, you will hit a tech fragment wall. And the wall will be getting rapidly harder and taller with each additional level. I expect that around weapon level 140 that wall probably reaches from the Caligari sector all the way to Holy Terra...