When the same control signal is used to enable two TPS4019x, it is not suggested to tie the ENABLE pins of the two TPS4019x together. The reason is as follows. Due to the process variation, the threshold on ENABLE pin which is 1.9V typical (3xVBE) is not exactly the same from part to part. As the voltage on ENABLE pin rises up, one of the two parts which has lower threshold turns on first. Then the ENABLE pin is self-clamped and the clamp voltage can be as low as 1 V with a 1-kohm ground impedance. As a result, the other TPS4019x cannot startup.
A possible solution is to use separate pull-up resistors after the enable signal's pull-up, e.g. to have a resistor pulled up to VDD with 2 separate pull-ups to each of the IC's ENABLE pins. So that
(1) When one TPS4019x turns on and the associated ENABLE pin is clamped to 1 V, the voltage at another ENABLE pin is still well above the maximum ENABLE threshold.
(2) The current into each ENABLE pin is limited to no more than 500 uA.
Regards,
Na