hi,

yes you may appear in two board exams as the same time of the year, however you must make one consistent decision like in which of the score card you would showed for admission to hire studies or for applying to job. you have to decide first between the two score card ,  and I suggest you to consistently maintain the same marks and score card through your whole academic career like bachelors, masters, phd and through your full professional career.

Doing this will not be beneficial for you in any ways. Also you can pursue boards in two different boards.

Goodnight!