Yes absolutely!
Molebens, the Paraclesis (another Moleben) and Akathists can be done either as liturgical services in Church or read privately.
One may even substitute the Divine Office by saying seven Canons with Akathists.
We may say these supplicatory prayers at any time for any intention (this hearkens back to the old Roman rule with respect to the Emperor - a subject always had the right to approach the Emperor with a request/need).
Fr. John Whiteford has a marvellous collection of these in English on his Orthodox Liturgical Resources site (just google that title).
Molebens can be done to any Saint for any intention, but the most frequent one is done to the Mother of God (Fr. Whiteford has the rubrics for a general Moleben with the necessary variant prayers).
There is also the Russian tradition of the “All Night Akathist Rule” where Canons and Akathists are prayed throughout the night.
The Ukrainian Orthodox married priest, St Jonah of Odessa, would do this rule daily. He once prayed over a blind child’s bed for nine nights straight and on the morning of the tenth day, the child could see.
Alex