How to increase volume of my turntable - pre-amp - amp setup

No, you need a phono pre-amp to go between your turntable and your pre-amp. The output of a phono cartridge is very low relative to a "line-level" component like a CD player or tuner. The output of a phono cartridge requires special equalization, as well as gain, before it is input into a pre-amp.

You can get a phono pre-amp from Pro-Ject, NAD, Parasound, etc., for about $100 - 150. You can find cheaper on e-Bay or at Parts Express, but I don't know how well they will perform.

Once you have a phono pre-amp in the system, the output when playing records and CDs will be similar.

@reubent is correct on all points. The last thing you need is a cheap device that boosts your output signal while increasing and adding noise in your system. And you don’t need more gain from your amp to the speakers, you need gain from your TT cartridge to the preamp.

Once you have a phono pre-amp in the system, the output when playing records and CDs will be similar.

This statement says it all. The output level from a cartridge is VERY low.

Yes, you need a phono preamp otherwise known as a phonostage. Given that your other components are so inexpensive you might search E-bay for an older Radio Shack phonostage. They can be had for ~$20.  Audio Technica made one that was selling for ~$50, you might search for one of those. I don't remember model number. 

If you are willing to spend more, Schiit Audio sells on for $129 that is highly recommended at that price point. You can also check out Needledoctor online.

Good Day Folks! Thanks for helping me out.

reubent, The Behringer preamp in my system is a phono preamp.

https://www.amazon.com/Behringer-MICROPHONO-PP400-Ultra-Compact-Preamp/dp/B0028QCYS0/ref=sr_1_8?s=el...

It performs well enough for my casual needs and increases the signal enough that when listening to a LP at full volume you need to talk louder when in conversation. But a CD  is much louder at full volume than a LP . You have to shout.

I want more volume from my LPs.

czarivey you wrote:

pick up phonostage with higher gain.

I wholeheartedly agree! How do I know which phono preamps have higher gain? How do you evaluate specifications? When I check out preamps I see these kind of specs:
Input Sensitivity: 3mV at 50K Ohms              
Output: 2V max (P-P) at 10K Ohms -
Input Sensitivity/Impedance/PHONO 3 mV / 50K Ohms

I have no idea how to use this information. Help!

noromance, you suggested a different preamp. I have looked at many of these but, as I wrote above, don't know how to evaluate. I assume a pricier preamp is higher quality but does higher quality mean more gain?

Search here for a choice at various price points.
https://www.amazon.com/s/ref=nb_sb_ss_i_1_5?url=search-alias%3Delectronics&field-keywords=phono+....

If I can't get a more powerful preamp this component  https://www.amazon.com/TC-780LC-Stereo-Booster-BLACK-VERSION/dp/B000RZXAHI  seems to be an alternative. But, as lowrider57 said I'd rather not introduce another component into the chain.

Am I on the right track? 

Which AT cartridge do you have?  MM cartridge gain is measured in milli volts (mV), usually running from 2.5 to 5 mV. Phonostage gain is measured in decibels (dB), Most budget MM ones usually run from 34 to 50 dB. Do you know the gain of yours? Knowing these values would help to derive the best cartridge/phonostage combination to achieve your goal.

A doubling of voltage provides a 6 dB increase in gain. A 9-10 dB gain is required to provide a doubling of perceived loudness. The output of your CD player is likely 2.something volts. Your cartridge/phonostage is likely putting out ~1 volt. Therefore the CD player provides ~6dB of gain over your cartridge/phonostage combo.