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
The specs listed are for the Phono Record Box E, which in addition to being a phonostage also serves for analog to digital (A/D) conversion of LPs.  The Phono Box is a phonostage only and thus less expensive $60, and yes, if its gain is also 40db it will boost the signal over your Behringer by 5dB.  This would not bring the volume up to that of your CD player however might be enough to satisfy your needs. The voltage supplied by the Phono Box would be about 1.7X that of the Behringer.  I believe Needle Doctor sells the Phono Box, they are good to talk to. Look them up online. 
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.