Headphone amp for vinyl?

Hi everyone -- I was wondering if I could ask for your expertise on this matter. My current analog setup is a VPI Aries/JMW Memorial tonearm/Lyra Delos cartridge, Parasound JC3 phono stage, Musical Fidelity M6i integrated amp powering Von Schweikert VR2 speakers. As much as I'd like to turn up the volume, I'm often unable to do so. I listen primarily to classical LPs. Is there a role here in getting a decent headphone amp to enable more enjoyable listening levels? If so, any recommendations for one that pairs well with vinyl?
I don't think that the source matters all that much, as long as you can get a fixed level signal from your integrated. One factor in choosing a hp amp is the phones you pairing it with. Lots of very good info on that at head-fi.org. I've been very happy my most recent one, by Woo Audio. Headphones are a very personal choice in terms of sound flaovor and comfort. I would recommend getting to a head-fi meet or an audio show where you can try out quite a few different options. I also think Cable Co. has a library of phones to try out.
I replaced my ancient Grado SR60s recently with a pair of SR80i. After considerable break-in they sound amazingly good. I also have a little Chinese "Bravo" tube headphone amp that works well and sounds great, although both of these items are so inexpensive they likely aren't even considered by most around here. Still...
If you like classical, some recommended brands are AKG or Audio technica (woodies). It also depends if you like Solid state or tubes.
Get yourself a pair of Grado 225i headphones and a Bellari 540 with a 7025 driver tube. The 225i works with all types of music. A great pairing for around $500.
Thanks for all your input. I actually already have a pair of headphones which I love, which happen to be Beyerdynamic T1's. I ended up getting a Burson HA160 headphone amp for a discount, and so far I really like it!