trickydude - I’m not apprised of brands and models, but can paint a basic picture that might be helpful. Bluntly stated, Jim Thiel’s designs had impedances that were too low, making them suitable for only robust amps rated to deliver power into a 2 ohm load. Big discussion as to pros and cons, etc. but that more thorough investigation requires study beyond this answer.
There are two major aspects of speaker loads germane to your question: impedance magnitude and impedance reactivity. A: The 3.6 would properly be rated as a 3 ohm load. B: to its credit, it is an extremely resistive (non reactive) load. Amps love resistive loads, so if an amp can deliver the requisite power into 3 ohms, then it should work. See Stereophile’s measurements in its 3.6 review for reference.
There is another set of issues. Mainstream mid-fi amps rarely delivered such power, at least not gracefully. Japanese designers invariably chose to enhance specifications (TIM, etc.) at the expense of sound quality. In today’s market, you would probably be best served by an American design rated or reputed for operation into low impedance loads. On the used market, there are suitable amps that sell for a fraction of their new prices.
I’ll share some quite limited amp thoughts. At Thiel Audio we used Classé, Mark Levinson, Krell, and Conrad Johnson. Audio Research came and went, as did Classé, but they have models that work well. I still use my 1990 Classe DR6 preamp and a pair of DR9 power amps. I also have an Adcom GFA555 II which is adequate, but less than best of form. A friend has a PrimaLuna integrated which is an excellent sonic match, and an inexpensive candidate. The new Benchmark gear is magnificent at its price.
There are lots of folks here with lots of relevant experience; but it’s all been covered and kicked around. I suggest you might skim this thread to see what surfaces. I recommend that you try what you have, making sure you keep the gain below audible distortion. Distortion melts drivers. Assuming the speakers have been tested and are running without problems, the key to progress is to assume the amp, rather than the speakers, are limiting your sound quality. This world has many interacting variables which are not easy to learn, teach or understand. With an open mind and some patience you have a speaker that can be very, very good.
Happy Trails