How to make low end digital sound "not terrible" on higher end systems?

Hi all,
So when I listen to my hyperion CD of Rachmaninov’s Vespers (Corydon Singers with Matthew Best) or The Eagles "Hell Freezes Over" on the below system it’s utterly fantastic. The Vespers is just amazing. I could go on about how wonderful it sounds.
However, when trying low end sources (my iPhone or streaming from Spotify) through the below system ....well, it’s essentially so terrible, it’s almost laughable. It’s just offensive to my senses and really can’t be listened to for any length of time as it’s just very annoying.Is there anything I can do to make it tolerable?
And here’s what I mean by "tolerable": when I’m exercising or just out and about, I’ve got some descent LG ear buds bluetoothed to my iPhone and while the music (either from files on the phone or streamed from Spotify) isn’t like the Vespers mentioned above, I enjoy listening to it. It doesn’t annoy me and I’m into it, I’m captured and can lose myself in the music. I’m "rocking." --I’m not gritting my teeth like I do when it’s played over my below home system.
What I want is to occasionally play a lower end source over my home system and not have it suck as bad as it currently does. ....To at least get it to the level of my cheap ear buds streaming Spotify.I know there are many reasons low end sources sound crappy over good systems but are there any fixes? Some EQ adjuster that’ll at least get it up to where my ear buds are? Or something else?Thanks!

PS Audio PerfectWave transport
Chord 2Qute DAC
Modwright SWL 9.0SE Preamp
Butler 2250 Amp
Modified Maggies (by Peter Gunn)
Are you hooking up the iphone to your Chord DAC? If not, that should help a ton. Otherwise, are you playing back lossless files from your iPhone (assuming not since Spotify is lossy)? On higher-end sound systems, I found that I simply cannot tolerate lossy files. They take too much information away to the point that they become shrilly, tinny, and bright... almost painful to listen to. My solution? I've since only listened to FLAC, ALAC and other lossless file formats... and I ditched Spotify for Tidal and never looked back.
What kind of files do you have on your phone?  Are they MP3?  Spotify streams in org vorbis, which is similar to MP3 
MP3 sounds fine to me as well through headphones or earbuds, but sadly deficient through a HE system.  Any system that will try to turn the pigs ear into a silk purse will do so at the expense of inaccuracy.
If that is really your goal, then I would get tubed equipment that is known for old fashioned tube sound (not all tubed equipment sounds this way anymore, but I’m talking Prima Luna, Jolida, maybe older Conrad Johnson) and try to expand the Soundstage and fatten the midrange.  Or, you could just stop listening to low rez recordings if you find them so offensive 
+1 @mahler

A tube preamp and try Apple AAC 256 from your iPhone. Spotify is not quite there in compression quality. 

If you are feeding the system from the iphone and other devices with Toslink cable, then all you need is to reduce jitter using a reclocker like the Synchro-Mesh.

I listen to lossy low-rez tracks streamed from Amazon Prime all the time.  With low jitter they sound amazing.

Steve N.

Empirical Audio

streaming and direct playback will be different no matter of the format. streaming is always very-very lossy. 
simple red-book cd will easily blow away same tracks played with streamer no matter of streaming resolution quality.
Maybe try a forgiving all-in-one system with some forgiving bookshelf speakers for background music and listening to your  poor sounding cds.   Keep your good recordings separate from the bad ones.
If you're using your iPhone to send music via bluetooth to the 2qute dac, then that's your problem.

Numerous ways to improve the sound, some mentioned above.

-Directly connect your phone to the 2Qute.
-Get a wifi streamer (chromecast, auralic, bluesound) connect that to the 2Qute, instead of BT.
-Tidal instead of Spotify

Any of those should produce much better sound quality.
Thanks for the replies.
I'm using wifi to stream (Spotify or music on my phone) to a Sonos Connect which is connected to the 2Qute DAC.
audioengr above mentions reclocking to reduce jitter.  I know nothing about it but this sounds interesting.  It would be easy enough to put one in between the Sonos and the 2Qute.Can one expect dramatic results from reclocking?

--I'm not trying to make these very lossy sources sound like my good cd's ...I'd just like to get my home system to sound as good as my crappy bluetooth ear buds and iphone when playing lossy music.I'd also really like to avoid a second "forgiving" system.
"streaming is always very-very lossy.
simple red-book cd will easily blow away same tracks played with streamer no matter of streaming resolution quality."

No my experience with streaming MQA sources from Tidal. Then again, it could all depend on the quality of the CD player and the streaming devices, so basically pointless comparison.

IFI Audio has a excellent usb plug in device ,as well as AC plug in
units that clean up the digital ,regenerate as well as clean up the power . And not expensive in the $100 range.
They’re still working on how to make digital from HIGH END sources sound good on high end systems.
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"They’re still working on how to make digital from HIGH END sources sound good on high end systems."

"They" are also working on making turntables and cartridges sound good on high-end systems.

I'll take my digital over LP's any day. No contest.

Steve N.

Empirical Audio

Tubes won't help.

The signal bears no relationship to the original signal and the lost information cannot be recovered.

Compressed audio is tolerable here as sonic wallpaper only either mono over a Boston Acoustics Solo or through 5-ch stereo on the HT.

Otherwise, fogedaboutit!
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Tubes won't help. The signal bears no relationship to the original signal and the lost information cannot be recovered"

This statement is completely false and reflects confusion, ignorance and/or misinformation about the nature, function and operation of vacuum tube equipment. While I accept and understand you're apparent distaste and dissatisfaction with tube equipment, it is by design and operation a simple, demonstrative and scientific fact that the output bears a distinct relationship to the input signal which can be proven by simple math. If you can not accept, understand, and acknowledge this simple, basic, and fundamental premise then explain to the rest of us where the vacuum tube circuit gets it's output if it "bears no relationship" to the input do you think it collects it's output signal from thin air?
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I own tube equipment.

I should have said "Lossy compression bears no relationship to the original uncompressed signal and the lost information cannot be recovered, therefore tubes will not help."

Tubes may soften some of the more egregious artifacts, but will not stop image wander. In some respects tubes make it worse because sound staging is particularly affected. In a great system with excellent 3d presentation, it puts me in mind of orchestra meets Cirque du Soleil