Turntable /Cartridge hum

I’ve written about this before, but the problem seems to have gotten worse.
I have the unfortunate combination of a Rega (modified RP3) turntable and a Grado (Sonata Reference) cartridge, both of which are known for hum issues.
Whereas the sound is fabulous to my ears, there is a loud hum that I can hear when I get close to the speakers.  Fortunately I can’t hear it when the music is playing, but I certainly know it’s there, and somehow must be affecting the sound.  Also, I’ve just begun to not even a sort of fluttering sound that was not there before coming from the speakers.
Can anyone suggest an even partial remedy for these problems other than getting rid of turntable or cartridge, or both?
Only problem is, I really like the sound.