Re Biasing a SS Amp?

First off the heat sinks are probably not designed to shed the extreme heat of running full blast Class A.
Since the item was designed for it's current design, the heat sinks are certainly NOT capable of dissipating Class A heat.
Second, trnasistor run better longer when cooler. One has to use special, or suitable transistors for Class A operation.
For example. the old Forte 4 was 50 watts class A, the exact same ampe in schematics was the Forte 6 a 100 watt output.
The company had to check all the transistors and pick the better ones for the Forte 4, and stuck the 'ordinary ones on the 6.
Why? because the Class A transistors were going to be running under much harsher conditions!!
So, yeah you CAN change the bias to class A. Whether the amp will survive?? is not likely. First it will always be overheating, second it will be killing transistors fast.
Other than that, no problem.
You CAN also have the class A to AB threshold raised a bit. Way safer than straight class A
But still, why bother?? The cost, the fooling around.. Just buy a different amp.

You don't say what amp this is so it's difficult to know. We also don't know if the outputs of this amp are bipolar or FET. That makes a difference. In a bipolar amp you can adjust the bias slightly higher so the amp stays in class A for a few watts more before switching to class B. Will it make a difference sonically? Doubtful. Will it prematurely age capacitors and other components due to the increased heat generated. Definitely. If you want a class A amp, buy a class A amp.

Over biasing a class AB amp will only produce more heat without any sonic advantage. About 150ma per the sum of all transistors per channel is about the ceiling for optimum performance. Converting to class A would involve redesigning the circuit altogether

In my opinion it will make it worse. It is called overbiasing. There is optimal amount of bias for any class AB amplifier. Increasing bias makes partial operation in class A but is increasing window of increased gain caused by the fact that two, instead of one, transistors are conducting. This double transconductance is called "gm doubling". Measurements of the same amp with different bias points (Douglas Self) show slightly increased distortions above certain optimal bias point. Overbiasing is not as bad as underbiasing but optimal bias is what you want. In addition class A amps sound better because since they don't have to be linearized so heavily negative feedback can be shallower. Class A amplifiers have gain, before feedback is applied, in order of few hundred while class AB amp gains go in thousands. Deeper feedback can produce TIM (transient intermodulation distortion) - basically an overshooting fast transitions, equal to producing odd harmonics in frequency domain. Also, as Hifigeek1 said, it might age prematurely capacitors, since it was designed for different heat dissipation.