If you'd like, you can measure the system now as is and try to make changes. But that'll be shooting in the dark. For instance, we know the tweeter is an LR2 slope xo at 2000hz. What if there is a big peaker at 2500hz? Maybe it's a break up peak. Maybe a rising response. If there is a big wide dip from 300 to 700hz, maybe the .5 woofer has to big of inductor. We don't know though.
The way coctostan described it is best. For now, might as well measure the system just to see what you have, if you'd rather start that way.
To measure, get the speaker as far away from any obstructions as possible. Even raise the speaker of the ground a little. Position the mic on axis with your listening plane at 1m (3.2ft) from the listening axis (tweeter most likely). If you have a very large are you can work in, back up to 1.5 or even 2m if you can. But you want to gate the measurements so there are no reflections from the room, so likely 1m will have to suffice.
Once you've done that, post the results and hopefully an expert can offer you some tips. I recently learned how to take measurements for a speaker. It's a lot of work. Getting them good is important. I have a small room. I moved ALL my furniture out of the room to finally get it right. You could almost say I was lucky my XO worked with my first measurements