私は今年何度か海外に行きました。 [SOURCE]
I have been abroad several times this year.
北海道へ何度も行った
I have been to Hokkaido many times.
本を何冊も読む。[SOURCE]
I read several books.
本を何冊か買いました。
I bought some books.
何杯か飲んだ後で [SOURCE]
After a couple of drinks
何杯もお茶を飲む [SOURCE]
Drink countless coups of tea
昔は、私がもっともっと若い時は、1日に何杯もコーヒーを飲んでいました [SOURCE]
(DeepL) In the past, when I was much younger, I used to drink several cups of coffee a day.
I cannot see any difference other than the one with も being emphatic.