In monogamy can a person be married to more than one person at a time?

It depends on the laws and customs of the country concerned.

The form of marriage you describe is called polyandry. It is the rarest form of marriage. Reportedly, the only societies practicing polyandry are Tibetan, Toda, Sherpa, and Marquesan. Polyandry may be legal some places where it is no longer practiced. And, I understand that Saskatchewan Canada has laws that may make it legal there. You can check the status of Polygamy in various countries using the link provided. Note that the link covers all forms of Polygamy (multiple spouse marriage). Many countries allow Polygany (one man married to multiple women), but do not allow Polyandry.