Well, there are preamps, and there are phono preamps. A simple preamp only amplifies signal, a phono preamp amplifies signal and changes its EQ to accommodate the RIAA curve. The OP has a TT with an integrated phono preamp, but perceives too low volume. He can add another simple preamp between the TT output and his main amplifier to increase volume. This extra preamp doesn't need to be a phono stage, it can be a normal preamp, as the integrated one has already changed the EQ. But he will end with too much volume increase if he goes this way.
I believe it will be better for him to stay with his equipment as it is, as long as the signal is not distorted nor clipped. But if he really needs more volume without turning knob past 12, he can bypass the integrated phono stage and use an external one with more output (and I think this is not possible with its TT). In this case, he can sell the TT and buy another one without the built-in phono stage, and purchase a more powerful separate phono unit. There are not expensive phono preamps on the market: Pro-Ject, Cambridge, even Graham Slee basic line...
He can also buy a more powerful amplifier... Or more sensitive speakers...
I still think the best solution is to stay as it is now, and listen to music with knob past 12, if the sound is not distorted.