Yes, you can do what you are asking about, but it will be pretty limited compared to having a stand alone DSP. Adding a DSP-408 between the head unit and amplifier will give you far better control over the system. In the mean time, I've outlined below what I believe you can do with the equipment you have. The configuration below will feed your tweeters with the front channels and your mids with your rear channels. Keep that in mind when you do your tuning.
ILX-107 Front Out > PDX-V9 CH-1/2 IN
ILX-107 Rear Out > PDX-V9 CH-3/4 IN
ILX-107 Sub Out > PDX-V9 SUB IN
You'll be using a combination of amp and head unit crossovers to get the bandpass crossovers you need on the mids. I would start with the following settings on the PDX-V9 and adjust as needed to dial everything in.
PDX-V9 CH-1/2
HP FILTER: X10
CROSSOVER: 200 (2kHz)
CH-3/4 INPUT: 3/4
PDX-V9 CH-3/4
FILTER: BP
CROSSOVER: 30 (Minimum - Make use of the head unit crossover)
PDX-V9 SUB W.
SUBSONIC: Depends on your subwoofer setup.
LP FILTER: 600 (Maximum - Make use of the head unit crossover)
SUB W. INPUT: SUB W.
(Note that the crossovers for the mids and subwoofer on the amplifier could be used in combination with the crossover on the head unit in order to hit your target curve/acoustic crossover.)
On the gain side of things, I would set the gain with on your subs and then adjust the gains accordingly to match for the mids (rear) and tweeters (front) accordingly. We will get into additional adjustment at the head unit below.
Use the TuneIt App as JMikeK mentioned, as it will give you the most control out of your head unit. In the app, I would make the adjustment settings as follows...
Crossover
Front HPF (Tweeters)
Level: Adjust as needed to match the level of both tweeters to the mids
Frequency: 200Hz (just some added protection on the tweeters, should be more than 36dB down from the amp X-Over anyway)
Slope: 24
Rear HPF (Mids)
Level: Adjust as needed to match the level of both mids to the Subwoofer(s) and tweeters
Frequency: 50-80Hz (Whatever works best, I'm guessing 63Hz)
Slope: 24
SW LPF (Subwoofer)
Level: Adjust as needed to match the level of the Subwoofer to the mids
Frequency: 50-80Hz (Start with matching the mid HPF)
Slope: 24
Time Correction
Use the actual measurements to the tweeters, mids and subwoofer to do the time aligment. Remember that the Front speaker adjustments will apply to the tweeters, and Rear speaker adjustments will apply to the mids.
Fader/Balance
You can use this setting to further adjust the level balancing between drivers. Fading to front will reduce mid level relative to the tweeters. Fading to the rear will reduce the tweeter level relative to the mids. Balance will do the same thing except it will adjust left vs right relative levels
Parametric EQ
I would wait to make any EQ adjustments until after you have everything else set. The EQ applied to all channels when you make the adjustments. If you have a mic and measurement software, I would do a spacial average of the entire system playing (mono pink noise or sweeps) and adjust accordingly. If you don't have a mic and software, even AudioTools RTA on your phone can help identify problem areas to be adjusted.
I'll leave it up to you to test out the other settings to see if they are helpful for your specific install or not.