I have (and had for a while now) two versions of CS on my machines- CS3 and CS4, CS4 and CS5.5, and now CS5.5 and CS6- no issues what so ever. However I never had an older version installed after I had a newer one already on the machine.
I’m with Tudor & Vishesh — you can have multiple installs (I have CS4, CS5.5, and CS6 installed on the workstation I’m on right now, and CS3, CS5, CS5.5, and CS6 on another).
I would highly recommend that you install them in order. If you have CS6 installed now, uninstall it, install CS3, then re-install CS6.
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just wondering if you ever managed to install CS3 on a machine running CS6? I’m about to try the same and wanted to check whether installing CS3 would remove CS6? I can’t remove CS6 first and reinstall as I no longer have the disk!