To increase the number of paper clips the electromagnet attracts, the students could take the following two actions:
B. Add another battery - Using an additional battery would increase the voltage, which would enhance the strength of the magnetic field generated by the electromagnet.
D. Increase the number of coils - Increasing the number of coils around the nail would also strengthen the magnetic field, allowing the electromagnet to lift more paper clips.
Thus, the correct actions are B and D.