4 ohm speakers on a Pioneer Elite SC-37 receiver?

The receiver will handle 8 and 6 ohm speakers. It is more powerful
at 6 ohms than 8. I would not hook up 5 or 7 speakers rated at 4
ohms. You may be able to hook up 3 front channels rated at 4 ohms,
if you watch the volume. However, this is not a reccomendation.

Not all 4ohm rated speakers are equal. Some - like Magnepan planar speakers would kill most any AVR you connect them to. Others like Emotiva which I used to own are fine with just about any AVR you want to drive them with. It all has to do with the impedance dips the amp experiences while driving the speakers.
I thought THX Ultra2 Plus would denote an AVR or amp that could drive 4 ohm speakers - apparently it doesn't.
Post on the Totem owner's thread and see if anyone is using an AVR similar to yours with any problems.

They may be doing the slider thing - 4 to 8 ohms average. If the speakers
do not dip below 4 ohms - then you have a better chance. Some 6 ohm
receivers can do 4 ohms - they just do it with less power. The Sony ES
series, seams to be like that.

Changing the load from 8 ohm to 4 ohm increases the wattage output of the AVR. As far as Totem listing the sensitivity at 8ohm, it could be a simple typo or it could be that Totem did not want to list 84db as the sensitivity since that is very low. I suspect it is not a typo. 84db 1W/1M is what the actual rating would be if the 87db 8ohm rating is correct. Speaker is only good for low level listening. Listening at 12db below reference at a distance of 13' you will need to feed the speaker 128 watts. So 12db below reference is about as loud as you will be able to go. Any more than that and you will get a lot of distortion from the AVR and speaker.

Added
This is assuming that the 120 watt rating of the speaker is not peak rating.

Bottom line - look for more power or different speakers.

Look in the Pioneer threads. Pio rates it to 6 ohms but it does pass the THX cert (dip to 3.2 ohms IIRC). Interestingly enough, it was reported in one of the threads that the ICE amp from which the Pioneer amps are derived is rated at 4 ohms; Pioneer rates them more conservatively (could be cooling or power supply capacity among other things).

My Pioneer SC-27 blows away my previous Sony ES (3400, I think) AVR for power, especially with all channels drivern, but that's a top-of-the-line Pioneer to a mid-range Sony so not a fair comparison.

Magnepan speakers are 4 ohms but a pretty flat load impedance; many of us are using them with Pioneer receivers (mine are on an SC-27). Dynamic speakers tend to be more efficient but are often a much worse (more variable) load. This is the first I've heard Magenpans are hard to drive -- have you compared their impedance curves? The bigest issue I've run into with Magnepans (in some 40 years of using them and working in this biz) is that they are inefficient and thus take a little more power, not that they are a harder load impedance-wise. Whatever.

FWIWFM - Don

I pretty much agree with you. I forget the Sony ES model number -
but they did rate their 4 ohm load about 20 watts lower than 6 ohms.
In this day and time the companies are being more conservative and
want to protect themselves. I am concerned about the 120 watt rating
on the speaker.

If your AVR is calibrated so that 0db is reference level then yes. Keep in mind that you will still be getting power compression at -16db/-18db and loss of dynamics.

My non-Elite Pio 1120 runs my 4 ohm ERD-1 surrounds without breaking a sweat at whatever volume I need. (then again, I rarely need to go past -20 to rock movies or music in my ht room).

But, of course, it all depends on the speakers. The ERDs are 89db at 4 ohms, so they're fairly efficient. Also, since they're just surrounds, they're not peaking very often.

I probably wouldn't go much higher than -15 with yours...