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Jon it is possible but cost wise, and efficiency wise it would be best to replace the entire air handler.
One issue you are going to have is the higher efficient coils available today are usually larger so a matched coil for the new heat pump will probably not fit in the air handler.This means we will most likely end up with a mis matched and in efficeient system
Any particular reason for wanting to keep the air handling unit?
The higher efficiency is derived in part by more surface area of the indoor coil. So where the existing coil is only about 21" tall, the new 3.5 ton coil would be about 31 inches tall, therefore would not fit in air handler.
So you would have to use a coil that would fit in the old air handler. Aspen makes several. WE would measure old coil cavity , then find a coil that would fit. I suspect something like the CA42A or B would fit.See below:
Then you would need to install a TXV metering device