Indeed, simply plugging in a Blu-Ray player to your existing amp will improve the sound of watching movies tenfold over your standard TV speakers (though make sure you get a Blu-Ray player which has analogue RCA outputs).
However, if you're looking to get surround sound, you'll need an AV receiver and to get the missing speakers (i.e. at least a centre, two rears and a subwoofer). You can either do this by adding to your existing setup (recommended if music is important to you and you're happy with your current setup for this) or you could replace everything with just a home cinema set up as someone else has already said - this could well be a compromise to your music performance however, so I would ensure you audition carefully before going down this route to make sure you are happy with that compromise.
Adding to your existing setup is easy enough, you'll need an AV receiver which has front pre-outs - this will allow you to leave your front speakers, CD player and your stereo amp as you are for music duties. You can then connect the AV receiver to the stereo amp using the pre-outs and connect the surround speakers and Blu-Ray player to this. There's a number of posts which go into more detail on doing this, but the main advantage is your music performance is uncompromised.
You then just need to get the surround speakers to match your Mezzo 6 fronts - Mordaunt Short's recommendation is to use the
Mezzo 5 centre, the
Mezzo 2 standmounters for rears and the
Mezzo 9 sub - this package has been reviewed
here by WHF and, with the right AV receiver, will produce a pretty spectacular home cinema setup from the looks of it! If you wanted 7.1, you could add another pair of Mezzo 2s or, if budget is getting tight, maybe look at the
Mezzo 1s for the surround backs. Again, auditioning is king.