Can I bi-amp with an integrated amp's Main-In, and a Power amp?

I think you're spinning your wheels....   Not much if any advantage

It can be calculated from the sensitivity and power capability specifications of the two amplifiers that the gain of the Nikko is approximately 29.8 db, and the gain of the power amp section of the Onkyo is approximately 23.6 db. ("Gain" meaning the ratio of output voltage to input voltage). Doing what you propose would therefore result in bass frequencies being over-emphasized by about 6 db relative to mid and high frequencies, which constitutes a severe tonal imbalance. And it appears that the Nikko does not provide a means of reducing its gain.

So to achieve proper tonal balance you would have to somehow attenuate the signal that is provided to the input of the Nikko by 6 db, relative to the signal that is provided to the input of the Onkyo. And although that could be accomplished by inserting one of several kinds of electronic devices between the preamp and the Nikko, it would seem likely to involve more trouble and expense than it would be worth.

Also, alternatively, instead of connecting the output of your preamp to the input of the power amp section of the Onkyo, you could connect the preamp to the input of the preamp section of the Onkyo, and use its volume control in conjunction with the gain provided by its preamp section to gain match the two amps. But you would then be putting a lot of circuitry into the signal path that wouldn’t otherwise be necessary, probably resulting in some degree of sonic compromise. And you may also be limiting the amount of power the Nikko could deliver to significantly less than what it is capable of, because while the current and power demands placed on each amp would be less than if they were run full-range, for proper tonal balance both amps would still have to output the same voltages (corresponding to the full frequency range of the signal), and chances are the Onkyo cannot put out as much voltage as the higher powered Nikko.

Finally, not all speakers which provide two pairs of terminals are suitable for biamping. I’m not familiar with the particular speaker you mentioned, but there are at least a few designs around in which the two pairs of terminals are either connected to crossover circuits that are either not fully independent, or in some cases may even be connected directly together internally. Attempting to biamp such a speaker would stand a good chance of damaging one or both amps, since their outputs would be shorted together via the speaker.

The likely bottom line: Don’t bother.

Regards,
-- Al

it wouldn't hurt to try and let your ears be the judge.

the result will be all the way out of tonal balance and not much of volume ranges you can listen to.
definitely no classical orchestral music can be handled. 
bad idea.
i'd suggest using only Nikko amp alone for your music. this amp will drive your speakers fine, much better than bi-amplified.

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