The main exception I can think of is upcycling - rather than reuse a product, you recycle it into a better product. This is most obvious with computational electronics, where a 10 year old computer is likely to use a lot more electricity to do a worse job than a new one. Unfortunately recycling old computers is hard. So a better example might be a resistive electric hot water tank. If you have one, and especially if it has a problem, it's very likely better to replace it with a new heat pump one and recycle the old one.
A similar situation could occur with noxious plants and firewood. I have stayed on a farm where they were burning their way through a stand of honey locust trees (Gleditsia triacanthos). Once they discovered the trees, they killed them all we cut everything we could into firewood then transported it back to the firewood shed. They ended up with more firewood than they could store for any length of time. So they lit the stove and just kept it running. That way they got unlimited free hot water (and hot, clean burn), where the rest of the muck just got bulldozed into a pile and burned (in a very dirty fire). Reusing or recycling that timber would not have been appropriate (the "trunks" were only ~10cm diameter). Some of it probably rotted from being stored out in the rain, but they had lots.
I wonder whether some permaculture green mulching might be considered a violation of the "reduce rather than reuse" rule. You're growing plants specifically so you can re-use them, by digging them in after harvest.
Stepping outside the whole framework, I have heard people argue that if you are buying 100% renewable electricity, using more than you need to is a good thing because it helps make renewable electricity profitable. My response is that you're better off donating money to those companies directly, or buying greenhouse gas abatement certificates and hoarding them. But that "use more because of beneficial side effects" argument is, in a way, correct.