My air conditioning system has a 2-layered (each 1") filter holder, definitely made for two filters. My idea, to improve the filter life and have the least air flow restriction, is to have the initial filter be a coarse particulate filter to catch the big stuff so that it doesn't clog the second filter which is a much more expensive allergen fine filter. Any objections?
Go for it. Your only worry should be too much filter resistance, but you have that potential problem now.
You could go for a washable filter as the first layer, then a MERV13 for the second layer. Or a disposable MERV6 or MERV8 as the first layer and MERV13 for the final. Expect to wash or replace the outer layer more often.
Your unit may have a sight glass indicating "filter replacement", if so watch it. If not, you could cobble in a manometer. Or experiment a bit with cardboard blocking the filter, and get a sense if you can hear the difference in pitch when the airflow is blocked.
You should check with the manuals for the A/C system to ensure that you are not doing anything outside of the recommended. They do make cheaper filters that are designed to basically protect your system and not have any health or comfort benefits to you. Here are a few from Home Depot: basic filter and slightly less basic filter.
However, keep in mind that if you go this route you will have different maintenance timings on the filters. The basic filter linked above needs to be replaced every month and the other needs to be replaced before 3 months. So it is something that will have to be put into consideration