HEPA filters. High efficiency particulate air filters are the best way to initially help. Buying additional portable air purifiers could also help. Keep the dust and pet dander to a minimum since this plays a big role.
Filters. One thing that you can do is upgrade your hvac filters. Most filters are merv 8 but a filter with a higher merv number (i.e. 10 or 11) will remove smaller particles more effectively. If you have an unusual problem like a shedding indoor amimal or an old air- leaky home, stand-alone hepa filtration systems are available. Make sure you check-our replacement filter costs before you invest.