I do not know of any audiophile level "integrated amp" that supports streaming. If you really want an all-in-one unit, you'll have to look at some of the home theater receivers, such as Marantz, Anthem, etc. However, you will not get the sound quality of the Parasound because they will use lower grade power supply that needs to provide for 8+ channels (instead of the 2 channels of the Parasound).
The only alternative is to get an external DAC or streamer. The Oppo Sonica (as an example) is a fine external DAC and will support Airplay streaming as well as a variety of other streaming. This will give you a very nice analog DAC source for anything (streaming, CD, Airplay, spotify).
Or you can look at just a streamer and use the DAC in the Parasound (using a digital cable from the streamer). There are a lot of options at different price points. There's actually a "Streamers" thread in the digital forum here that you should read through.