much/a lot/ a bit
Dad promises he’ll live ... (healthy).
Dad promises he’ll live more healthily.
My brother promises he’ll cook.... (good)
My brother promises he’ll cook better.
She/speaks English fluently/he
She speaks English a bit/a little more fluently than he.
My grandfather promises he’ll speak..... (quiet)
My grandfather promises he’ll speak more quietly.
My grandmother promises she’ll drive..... (slow)
My grandmother promises she’ll drive more slowly.