how to learn piano as an intermediate musician?

i have already played guitar and saxophone for about 4 and 3 years respectively, and would like to consider myself to have a pretty good understanding of each. i also understand a lot of music theory, and can play basic chords on piano. but how do i get. good? i mostly want to learn in order to write songs, because i often feel like writing only on one instrument (guitar) is my greatest weakness and would like to learn piano to solve this. generally i think i've came to that conclusion because the few songs/chords i have written on piano generally sound different than when i write on guitar. not necessarily better, but different, which i think gives me a solid amount of variety in my song writing. i guess i just think about songwriting different from each instrument. anyways thats it i think.