 If you liked
Re:Zero kara Hajimeru Isekai Seikatsu
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 ...then you might like
Seishun Buta Yarou wa Yumemiru Shoujo no Yume wo Minai
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- the main character (male) is surrounded by female friends, but it isn't a harem
- the main character is attracted to the main girl who holds a high status position (actress/model, candidate for royal selection)
- the main character harnesses a form of time travel to rescue the main girl
- both animes have a side girl in love with the main character. the side girls in both animes have similar personalities and are voiced by the same person.