Intigrated Amp Dilemma

A little background:

I am currently using a Parasound Halo Integrated amp driving a pair of Golden Ear Triton 2 speakers. I noticed when getting the volume up to a really good level, the amp strains a bit and the sound gets thin.  I am talking at most 93-95db but usually I listen at less than 87db.

Very shortly, I will be moving my Golden Ear Triton 1 speakers into the system where the Triton 2 speakers resides as I am taking delivery of the new GE References in a week or two. I do not think the bigger Triton 1 speakers will be a great match with the Parasound integrated, I will probably sell the Triton 2 speakers.

I am thinking of buying a better sounding integrated with a bit more power and more reserve power. I would need 3 line inputs (single ended) and a built in dac. I am NOT interested in any Class D amps. I want to keep it around 5-6K new Can I be pointed in the right direction please?

Thank you!