• Neither of those are good options.

    Unsure of what you are trying to achieve here: Quality? Volume? Extra room capability? Ability to drive esoteric speakers?

    In general you should not put an amplified output into an amplifier.

    It seems your extra amp thing is just a power amp, with no pre amp volume control. Taking the headphone out into it will probably work OK, bit will almost definitely mute the speaker output of the main mini system. It might make it a bit louder. It might be of better quality (but probably not). It probably won't give you an extra room capability.

    The mini system will have some kind of (undoubtedly shit) headphone amplifier that drives that headphone socket. This signal will then be munged through your outboard power amplifier. The resultant signal is unlikely to be any "better" than the speaker output of your mini system. It might be louder. It might be capable of driving a low sensitivity speaker.

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