Integrated multi channel amp

Is there such a thing?
Yes, there is such a thing, although I have not seen it marketed by high-end brands, like Proceed, Krell, etc. Yamaha, for example, has a model called DSP-A1, or its latest version DSP-AX1, which is essentially their top-end receiver without the built-in tuner, but has all the surround processing modes for movies. Then, of course, this unit sounds like what you would expect from a receiver. Hope this helps.
Unless you cannot have a built in radio, you could try a receiver from or BK.