I am curious as well what steamer and products you are using?
I use a Miele C3 Silence vacuum cleaner. It's the cheapest (~€220) Miele vacuum cleaner that has top (A class in EU) filtration. More expensive models just buy you more accessories. Sadly, Mieles are super expensive in the US, and you can't do arbitrage due to different voltage. Nilfisk made in Denmark used to be extraordinary, but now they are pretty mediocre. /u/touchmyfuckingcoffee is a very famous vacuum technician in Reddit, and he recommends Miele and Riccar. He doesn't like bagless. Neither do i. Worse filtration and a mess to dispose if you are allergic.
I use a Coway 1008 DH air filter. It's cheap (€400), efficient, and uses low energy. IQAir has great reputation, but in some tests it has shown mediocre performance [1]. Perhaps these tests are not measuring particles in the smallest range, where IQAir claims to excel. I've seen some guys from IQAir at HN, perhaps they can clarify.
For house cleaning I use stuff from Sonett. Bio-D is also good, cheaper and easier to find. I also use probiotics from Chrisal. In the US, these might not be easy to find. I'm sure there are equivalent brands there. Check their ingredient lists. Bio-D cleaning stuff is so safe their hand soap is basically the same formula as their countertop cleaner. Many items are certified by Allergy UK.
I'm happy to hear any other recommendations from fellow allergics. I also found a two-stage filter for my shower (Sprite + Vitamin C Sonaki) did wonders to avoid spraying chlorine into my airways and reduce inflammation and itchiness.
It's understandable. On a small machine with little power, if they put a better filter (more resistance) the vacuum is not going to have much suction.
I'd like to add a me-too. We bought a Kärcher SC3 to remove old wallpaper when we moved to another apartment (IIRC the price of hiring a steamer for a couple of days made buying one attractive). We use it now to clean our tiled floors, the bathroom, etc. and it has been excellent. The hot steam removes most stains without much effort, it works without detergents, and it is far less work than mopping the floor.
Are you talking about other filters to filter the larger particles, and carbon filters? Because aliexpress sell them too.
The product page for the model recommended in that wirecutter article even has a cutaway view, showing that it's just a HEPA filter + carbon filter + fan.
But yeah if you don't care how they look or how noisy they are just assemble one yourself and blast it on max. That's what I did for two years in China and it worked (had a separate particle counter to measure PM).
In any case, they use little water. Like 1 tank for 90 m^2. You can always buy distilled water, or use water from your osmosis filter.