is it possible to have two diplomas from two high schools

Hi, Does anyone know whether there is a downside to have two diplomas from two different high schools? the background is that a kid is going to get a high school diplomas from his public high school, say in 2016, but planned to attended PG in a private school in 2016-2017, the private school suggested him to just repeat 12th grade and take the diploma from the private school... Also it is possible that for the 2015-2016 school year, the kid would be missing one course for the graduation requirement for the public high school, hence the kid may not graduate in 2016, but will do an online course in the summer of 2016 to fulfill the public high school's requirement, hence gets his diploma in 2017. it will mean getting a diploma from the public school and the private school separately in 2017.... Is it possible? is there any downside? thanks