Possible to aim for public/private jobs concurrently? Forum

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Right now I am considering several fields of law, including biglaw, energy, prosecution and tax. Is it possible to take classes/internships that allow me to pursue multiple options -- especially both public and private at the same time -- without seeming off putting to employers. Will private employers be concerned about govt internships and pro bono volunteering on a resume? Will govt employers be concerned about a biglaw SA? Essentially, I am asking whether I can have the best of both worlds by trying to do very well with regards to GPA, but also volunteering and doing govt internships throughout the year. At the end of the day, I just want to be employed as a lawyer, and I'm willing to do whatever it takes to make that happen.