Okay - so you want to create your own piano arrangements by ear and make them more interesting. I can relate. I have too many other things I want to do in my life to learn to read music and I'm cursed/blessed with the ability to play by ear (although piano is not my main instrument).
As you have probably seen, popular sheet music scores written for piano often include the single note melody line (for the vocals or whatever instrument will play the singers part if there is no singer) in addition to the bass and treble clef for left and right hand piano. The treble clef for piano incorporates the melody into it but adds fills and harmonizing notes and sometimes octaves etc. to make the arrangement more interesting.
But from your question, I gather that you are like me and don't read music and wish to emulate something similar by improvising and creating your own arrangement for right hand.
Here is what I do. I play the chords or a bass line with the left hand, and with the right hand I place my fingers over the keys I would play if I was going to play the underlying chord for that measure or passage with the right hand. I will usually position my hand as if I was going to play a four finger version of the chord (full octave if a major or minor chord). In most cases the melody played over a particular chord, will contain several notes from within that chord and any notes not actually in the chord are in the scale for that chord.
Then depending on the song, I might play the melody note along with a 3rd or 5th or octave and I might play some arpeggiated fills in between the melody notes where the singer would pause. With my right hand starting with the fingers above the chord, I am always able to easily find and reach the main melody notes to incorporate into whatever harmonizing or arpeggiation I am choosing for that song. It's the same concept that touch typist use when they position their fingers on the home keys. By starting on the "home keys" your fingers will be above most of the keys you will want to play over the chord you are on - and will be in position to easily reach any others.
Sometimes you might want to use an inversion of the chord for the right hand. The inversion you use might depend on which direction the melody is going in the next measure or with the next chord change.
Sometimes in between melody notes I will do an alternating rhythm playing the chord (or a 3rd or 5th) with my right hand and an alternating bass line with the left or even alternate playing the chord with left and right hand the way a drummer plays a pattern by alternating with left and right hand. It all depends on the rhythmic feel of the song you are playing.
In many songs, it's good to add a transition fill between chords to lead from one chord to the next. Depending on where the melody is going, these transition fills might start high and go lower or vice versa.
One other thing I usually do is apply the same concept to the left hand because simply playing the chord the same way over and over can be boring too. So I form the chord with the left hand and play different parts of the chord in between downbeats where I might play the full chord. For example I might play the full chord on the downbeat or the accent beat and the fifth of the chord on the up beat to keep the rhythm. Or alternate back and forth between a third and an inverted fifth playing the root an octave above the fifth.
Also, I find that if I am playing on the really bassy end of the keyboard, too many notes at one time in a left hand chord sound a little muddy to me. So I play a portion of the chord and alternate between the upbeat and downbeat.
This is a rather simple method for improvising on piano and I am sure more accomplished pianist might find it too elementary. But it works for me. And might be a good place for you to start.
Have fun.
