Focal Aria 948

The Parasound A21+ is a hugely (!) more powerful amp than the Pioneer 1250. 

I have 936’s (6” woofers vs 8” in your 948’s) and the bass is outstanding. Please note that the impedance curve drops below 3 ohms in the mid bass region. With a PrimaLuna integrated and a Mac MA352, I’ve enjoyed those speakers immensely. I even drove them with a vintage Sansui AU717 with excellent bass. An alternative might be Revel f208’s…similar price point.

 No way that Pioneer  amp is doing them justice. Maybe consider a better amp before you ditch the speakers. That being said, this past spring I purchased a pair of Salk Song Towers for a second system. I hooked them up to my main system just to try them out. To say I was quite impressed would be an understatement. Very musical speaker that just made music. Left them in for 2 weeks till wifey said 2 pairs of speakers in LR was too much. Great speaker IMO, but Im not sure your amp would do them justice either. Good luck in your quest.

Honestly in this price range/speaker size you really need subs. An active crossover that allows for a highpass is really the key to good bass with domestic size/cost speakers. 
 

I have owned some of the products recommend in this thread and they all lack bass slam and extention. While Focal and Harman make great speakers they both roll the deep bass off for efficiency, or to keep the box small. Harman specifically seems to do this with both Revel and JBL these days. I own/have owned Revel,JBL,Focal and Klispch so speak from direct experience. 
 

Once you have a true full range system there is no going back. 

I currently have them running on my Antique Sound Lab Monoblocks Better than the SX 1250.  But still not the bass I would like.