My answer is valid regarding Brazillian Portuguese.
You can do this in several ways in Portuguese. The language molds itself to the intention of the speaker, and sometimes the poetic effect is achieved not by the use of this or that word, but by the whole. I'll give some examples.
"Alguma", while normally translated as "some", can have the effect of many when it starts a construction like the ones you propose.
- Many a celebrity today did not graduate high school.
- Alguma celebridade hoje não se graduou no ensino médio.
Normally when used this way on the spoken form, alguma gets emphasis, being pronounced with the start of the word a bit slower, like "al-guma".
Other option you have is going with "Não são poucos/poucas". This is directly translated to "not a few", and is used to call attention to a quantity that is above average.
- Não são poucas as celebridades que não se graduaram no ensino médio.
You have to pay attention to the concordance on this form.
"Tantos/Tantas" can be used to denote a great quantity of anything when used to start a given phrase. It creates a bit of poetical effect, and normally is not seem on spoken form, being more common on literature. Those words should be used when the phrase is connected to something else that gives more context or continue the line of thought somehow.
- Tantas as celebridades que não se graduram no ensino médio, servindo hoje de exemplo para jovens de que o sucesso pode vir fácil quando...
"Tantas"/"Tantos" get weird fast if your context doesn't add relevant information to the text.
"Numerosos são "/"Numerosas são" - Functionally equal to "many a". Translates directly to "Numerous are", and is pretty rare on spoken language but relatively common on literature.
- Numerosas são as celebridades que não se graduaram no ensino médio.