I personally use a TC Eclectronic SpectraComp placed as the very first thing in my signal chain after the bass, dialed in to give me extra punch and bite, but blended in parallel with clean signal, in fact, something about whole 70% of clean signal on an average between the 3 frequency bands of the compressor, and fairly low compression ratios as well ,which the toneprint editor allows for, resulting in a compression that as said adds a great deal of extra punch and snap, but almost leaving my playing dynamics 100% intact.
Then as one of the last things in my signal chain, followed by some quite minor EQ adjustments, but otherwise right before my cab sim and preamp, I use another subtle compression from my Zoom MS-70CDR, which in fact is the model emulating the dbx160A rack unit, no idea how accurate it does that, but it works extremely well on bass, but again dialed in so it practically doesn't effect my playing dynamics, just tightening up the signal a bit, with a compression ratio of 2.5 and a fairly high threshold.
And both with a sufficient slow attack that they actually enhance the transient slightly rather than killing it, hence the additional punch and snap..
This works extremely well for me, and it is not squished in any possible way, as said my playing dynamics are left almost completely unaffected, just making my tone more punchy and snappy and tightening it up a bit.
The key to using 2 compressors though here is being subtle, but if you know how to use them in my opinion it will often give better results than just using 1.
Using all 3 would probably be overkill though, I'd say try using the Keeley as the first thing in your signal chain, right after your bass, and then the dbx160A as the last thing, right before your amp, or eventual even in the effects loop of your amp, using a fairly subtle setting on both, and turn off your amp's build in compressor.
Only if you want very squished sounds.
Far from necessarily, you'll only get a squished sound from using 2 compressors if you either want to, or if you don't know what you are doing.
I as well as most people familiar with music production would disagree with you.
More subtly/moderately dialed in using two compressors, one at the start and one at the end of your signal chain, will in many cases give favorable results.