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


Hi. Good Day to you all! My first post and first visit.

I have a cheap Scott turntable equipped with a low priced Audio-Technica mm cartridge through a cheap Berhringer pre-amp into a Logitech Z-680 speaker system. I also have a CD player separately into the system.

The volume output from the speakers is markedly lower from records than from CDs. I suppose that CD medium might be a little louder (the loudness war thing?) than vinyl but this seems to be an output problem not a difference in mediums.

I would like to increase  LP volume. How can I do this? Can I get a higher output cartridge for my turntable? How about a pre-amp with higher output? The Logitech speaker system seems plenty powerful.

I've researched but can't seem to find an answer that I understand. 

Thanks!

128x128rajastrums
Thanks mesch! I'll get in touch with Needle Doctor about the PRB E
In case there's any confusion, the recommendation is for the Phono Box E... not Record Box. And I don't see it listed at Needle Doctor.
https://www.amazon.com/Pro-Ject-Phono-Box-Preamplifier-Black/dp/B01CZW87HS/ref=sr_1_4?ie=UTF8&qi...

Technical specifications Pro-Ject Phono Box E   $59.95
* typical for MM or high output MC cartridges
Input capacitance/input impedance, MM:47kohms/120pF* Gain:40dB
Output voltage typically:500mV/1kHz at 5mV/1kHz
Noise floor:88dB (A weighted)
THD:<0,05%
RIAA-equalisation curve accuracy:20Hz - 20kHz / max. 0,5dB
Input:1 pair RCA/phono sockets
Line-level output:1 pair RCA/phono sockets
Outboard power supply:18V/500mA DC
Power consumption:20mA DC
Yes, the ProJect Phono Box E.  Has 40dB gain. Seems likely the go-to phonostage at that price point.  Guess not sold by Needle Doctor, sorry. 
I see it at amazon and other places.

Thanks to everyone for your help. I have learned something here!