La expresión española "cada vez más" equivale en inglés a los dos comparativos del adjetivo.
The film is becoming more and more interesting / La película se vuelve cada vez más interesante

1. We can repeat comparatives to say that something is changing.
   • These exams are getting worse and worse every year.
   • She gets more and more beautiful every time I see her.

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Additional points

1. We can modify comparatives with much, a lot, far, a little, a bit, slightly.
   • Bob is much richer than I am.
   • My mother's hair is slightly longer than mine.
2. We can modify superlatives with by far, easily and nearly.
   • Mario's is by far the best restaurant in town.
   • I'm nearly the oldest in the class.
3. We do not use the with the superlative if there is a possessive.
   • His strongest point is his ambition.
4. If the second part of a comparative or superlative sentence is clear from what comes before or from the context, we can omit it.
   • Going by bus is very fast, but the train is more comfortable.