You could get ten different answers from ten different people because it really comes down to are you satisfied with the sound. Since your asking I would assume not so IMO yes you do need to buy a amplifier. Although the 876 is a fine A/V receiver it isnt rated at 4ohm, 6 is the lowest, not only that but onkyo power ratings always rate the power per channel with only 2 channels driven. Meaning your attempting to power 7 speakers and its rated at only 2. So the numbers arent nearly as high as what you may read, it would be more like 75/channel which is not enough to really use the full capability of the speakers.
I have a similar setup with a 7.1 polk lsi series setup and I recently purchased a emotive 3 channel beast because the same question. Now I'm only powering the front and my onkyo 705 powers the rears but I have to say its quite impressive. Not from a volume standpoint, although it can get a little louder then before but from a clarity one. The highs are a little higher and clearer up there and the low and mids are where they should have been. All your doing is starving your speakers of power which if they clip you could have a serious problems.
I would suggest a 3 channel amp to start with for the front and see if you really notice a difference. But at this point with how much money and time you have invested in your HT its prolly worth the purchase. I would only buy the xpa series tho, better components than the UPA series IMO.
Look at the testing they never go lower than 6 ohms. Also power numbers are rated when only 2 channels are driven. Try added 5 more and lower the ohms. That is hardly enough to handle power hungry speakers. Why take a chance of clipping.
The 876 receiver is about as capable as it gets in any avr to drive power hungry speaker and yes to all above it is rated at 4ohms, check the manual and should not have any issues unless it's being driven to very loud levels in a large room.
Whether you need an amp is up to you, your listening levels, speakers and the size room you have to fill. I personally would be happy with the 876 powering those speakers and not feel the need to add anything, but again that's up to you. If your asking the question now you mise well go ahead and do it as you'll always wonder so why not answer the question for yourself and put your mind at ease.
Although the 876 is a fine A/V receiver it isnt rated at 4ohm, 6 is the lowest, not only that but onkyo power ratings always rate the power per channel with only 2 channels driven. Meaning your attempting to power 7 speakers and its rated at only 2. So the numbers arent nearly as high as what you may read, it would be more like 75/channel which is not enough to really use the full capability of the speakers.
You have no idea what you're talking about learn how to read the review. haha 55 watts a channel at 4 ohm yeah thats plenty for a speaker rated at 250. Not to mention the bench test you provided is with a 8ohm load not 4. haha wow you need to stop drinking the onkyo koolaid. Go ahead and clip those speakers buddy.
The Onkyo is actually 4 ohm stable. Its a very stout multichannel amp. It will more than do the job. THose Polk speakers by the way do not put a true nominal 4 ohm load on that amp. More like 6-8 ohms over the useable frequency range.
I have just ordered the Onkyo sr876 to run with the Polk lsi15 floor standing speakers. I will be hooking a PS3 to the receiver as well. I am attempting to hook them up myself, but I am close to illiterate when it comes to electronics. Any advice is much appreciated.