It is possible, if they both selected "someone else can claim me as a dependent on their return," which releases their dependency exemption. Otherwise your e-filed return will get rejected.
Here are the 7 test for claiming a dependent:
1) You provided more than half of their financial support. More info
2) They made less than $4,050 in gross income during 2016 unless they are a qualifying child (under 19 OR a full time student under 24 OR permanently disabled)
3) They live with you or they are related to you.
4) They are a U.S. citizen, resident alien, national, or a Canadian or Mexican resident.
5) They aren't (or won't be) claimed as a dependent by someone else.
6) They aren’t filing a joint return with their spouse.
7) You are not being claimed as a dependent on someone else's return.