Clearly, up to 300mA may controlled by the '328 IO pins if the current is spread around.
Absolute Maximum Ratings*
DC Current per I/O Pin ................................................ 40.0mA
DC Current VCC and GND Pins................................. 200.0mA
('328P has two Vcc and two Gnd Pins)
I guess you are assuming that 200ma limit is doubled because of two sets of Vcc and ground pins?
That is not my take, my take is that 200ma total is a absolute max package rating. But I guess there is room for misinterpretation on either of our parts.
Lefty