Connect multiple pins to same VCC using breadboard
You have basic misconceptions there:


Vcc is the power input (!) for the Atmega, not an output to provide current to other parts. Your power supply (whatever you use as one) should be connected to every Vcc pin at the same time. Sure, the Vcc pins are internally connected, but the Atmega has multiple of them, so that the needed current does not have to flow through a single pin. Also you don't want to draw the current for peripherals through the Atmega chip itself (which would happen, when you connect the power source to one of them and the peripherals to another). So every device in your circuit, including the Atmega, has it's own Vcc pin, which needs to be connected directly to the power supply. That is ok and correct, as long as the power supply can provide enough current for all components. If it doesn't, you need to buy a power supply, that can.
When connecting device to one pin, the number of devices is not imporant. The current draw is what is important. For example let's take simple digital output pin of the Atmega. It can provide up to 20mA (recommended value; max. 40mA for a short time). We must no exceed that value. So we can connect 1 device, that draws 20mA, or 2 devices, that draw 10mA each. Or 100 devices, which draw 0.2mA each. The number is not important, only the total power draw. The current will drop, when you draw more current, that the source can provide. In that case often the source will be damaged or at least go into thermal emergency shutdown (as for the voltage regulator of a genuine Arduino).


So the Todo for you: Connect every Vcc pin, that you have, directly with the power source.