there are 2 standard aspects to this:
-if your source has high impedance, the signature of the 846 changes following the impedance curve of the IEM, so source of higher impedance will make the low end louder and the 5khz area recessed. it can amount to several db depending on the source's impedance. that's a personal preference and such a change alone can feel like a very different perceived sound. most likely what's happening with the AV receiver and the louder bass.
- the amplifier section of whatever you use with the IEM was built to work nominally under a given set of conditions. the issue here is that the 846's impedance goes as low as 5ohm. imagine the electricity flowing, the impedance of the IEM is what opposes the flow, some of that energy is used to move the drivers, some will be dissipated as heat, and in the end the amp provided energy to be used by the IEM. when there is almost no impedance like with the 846, there is nothing to stop the flow of current. almost none of the energy is used/dissipated by the IEM, and it all comes back to the amp section of the device. the situation is much closer to a short circuit than it is to typical headphone/IEM driving. while there is little risk of something melting in the amp from such a tiny power(because the IEM is so sensitive you never push the voltage anywhere significant), it doesn't mean the amp section enjoys the ride. it can go from the device getting hot, and the objective measurements going down(increased crosstalk, increased distortions), to simply sounding like something is very wrong.
sadly there is very little ways to know how a device will behave with the shure because nobody measures devices into such low impedances. you're lucky if you can find a device measured into 16ohm. so something as crazy as less than 5ohm around 5khz like the shure has, it's a gamble each time. and it's very possible that the sound you don't like with your AV receiver comes from significant distortions in the 5khz area where the impedance is so low. if that's the problem, rising the volume level could make it audibly worst.
you could try to get the signature without the distortions from another source using some EQ, for the low end alone, you can probably replicate the effect of you receiver using a low shelf like this
the amplitude would depend on the impedance of the device so you'd have to try a few values, and the bass boost should start slowly going down a little before 100hz, but then again you might want to set the slope to your taste.
an alternative would be to get an impedance adapter. find a fellow DIYer who would do it for you, or maybe you can still get such things online, I bought some a few years back that were supposed to be er4 to er4s adapters, and after contacting the guy, he agreed to do any resistance I wished for. it's very basic stuff, one resistor in series for each channel, the plug is most of the cost.
anyway if you can find out the impedance of your AV receiver(on the headphone out!!!!!!!!) and the output impedance of your actual device, you could get such a resistor plug to compensate the difference and get your bass like it is on the AV receiver. I know that's a all lot of conditions to meet, but just to say that it is doable.