Well, the current should be discussed based on different circuit (Series circuit & parallel circuit), which is definitely in line with Ohm’s law.

In a series circuit, I=U/（R1+R2), if the voltage stays the same, with the increasing of resistance (more loads are added), the current will reduce correspondingly;

In a parallel circuit, I=U/（R1*R2/R1+R2), the resistance will also tend to reduce finally.

PS: Even the current is going to reduce eventually, their actual operating principle are various.