I would say it's all about context and what role the piano is playing. If the piano is supposed to be the focus I would not do too many cuts to the piano aside from corrective eq and maybe boost some mid-hi ~ hi freq to bring out the presence. If the piano is playing more of a supportive role I'll cut anything and everything I need to so it gets out of the way of other instruments and only occupies the space that's intended for it. Just my take on it, interested to hear others thoughts...

Thank you!