the speakers I am using are in my signature, the SVS S series with bipole rear surrounds. I would post individual specs later tonight, currently posting from cell phone. I will also switch to 8 ohm mode and try it out.
The trouble is, when I googled what you have in your signature, they show up as 8 ohms nominal but in your opening post you said you had 4 ohm speakers.
http://www.svsound.com/index.php?page=shop.product_details&flypage=flypage.tpl&product_id=25&category_id=12&vmcchk=1&option=com_virtuemart&Itemid=11
Nominal impedance is loosely defined, apparently there is a Europen standard (forgot the number) that says it is the impedance at around 1 kHz. So yes, most speakers rated 8 ohms nominal will dip down lower than that at certain bands but that is
typically not the same as one that is rated for 4 ohms nominal. Manufacturers such as Onkyo certainly knows that and therefore when they rate their AVR (mid range to flag ship models) for 8 ohms they already allow for those ineviable dips. That's why lab measurements conducted by HTM, HCC, S&V consistenly show such AVRs would put out much more power into 4 ohms but they won't do it simultaneously into all 7 channels on a continuous basis. That does not mean everyone needs to rush out to buy external amps. If that's the case why do we even have such a thing as AVR? There are people who will exaggerate this for various reasons, one being to error on the safe side when giving advice. I mean, it is easy to spend someone's else money.
In your case, I don't think I am the only one who will tell you the 876 happens to be one that does not have weak amp section (in relative term). SVS is first and foremost a speaker manufacturer so they may not necessarily be familiar with your particular Onkyo model, hence their 'cryptic' reply, i.e., if in doubt go get an amp. Well anyone can tell you that and that will be a safe bet.
They did suggest may be you should ask Onkyo. If you do, I will bet Onkyo will tell you the 876 can handle your speakers unless you have a very large room etc etc.... They may advice you to leave it in the 4 ohm setting for liability (UL/CSA/ESA) reasons. That will be fine too just that you have to turn it up to -10 instead of -13 for the SPL you like to enjoy. Even at -10, you should have enough headroom for most music and HT contents but if you can leave it at -13 or lower that it is better. I remember seeing on Denon's website FAQ section that they say there AVRs can drive 4 ohm (again, nominal) speakers even though their specs do not say that except for the AVR-4311 that is officially specified as 4 ohms capable.
I think my next step will be actually setting the db level with a meter instead of depending on Audysee.
You can easily check to see if Audyssey has trim the level of your L/R/C down to balance with the surround channels but it is definitely a good idea to use a SPL meter to find out what level you are listening to when the volume is set to -10 (set to 4 ohms), or -13 (predicted) when you set it to 8 ohms. Please let us know your findings.