Which of the following components should be added to an inductor to increase the inductance?
Why Inductors combine like resistors: in series the total is L1 + L2 + ..., so adding any inductor in series always gives a larger total inductance. In parallel they combine reciprocally (1/Lt = 1/L1 + 1/L2), which makes the total smaller than the smallest inductor. Capacitors do not add inductance at all; they store energy in an electric field and in combination with an inductor form a resonant circuit.
Watch out Putting another inductor in parallel is the tempting trap because more of something feels like more inductance, but parallel inductors divide down, just as parallel resistors lower resistance.
Inductors act like resistors: series adds up, parallel divides down. Capacitors are the mirror image.