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.