I should clarify what I meant. The current in the entire circuit may increase, but not the current through each battery. Let's say I have a battery with a certain voltage linked to multiple resistors in parallel. V = IR holds for batteries too, and because all batteries have some finite resistance, there is a maximum current that the battery can hold. So If I keep adding resistors parallel to this circuit, eventually the battery won't be able to supply the current to all the resistors. If I add a second battery parallel to the first one, then connect this combo with all the resistors, I double the maximum current or capacity. The current from each battery would meet at some point before being distributed to all the resistors or appliances in a real world situation. This sort of goes beyond the scope of the MCAT, but that's basically why batteries would be connected in parallel in the first place, to increase maximum current. In an ideal world, batteries have no internal resistance, and thus infinite current can go through them, and the concept of batteries in parallel would be meaningless.
I'm trying to figure out how to reply, so please forgive me if I come across in any manner other than polite here. Basically, what you have said here is just not the reality.
Voltage sources (such as batteries and galvanic cells) are added in series to increase the overall voltage (because with galvanic cells for instance, there is an upper limit to the
emf of the reaction). Three 1.5-V cells in series would allow you to have 4.5 V. That part I think we all agree on.
lixx669 is right on the mark with the fact that parallel batteries of unequal voltages would form a short circuited loop (one battery would dominate the other), such that the resultant voltage is some value between the voltages of each respective battery. In the easiest case, when the voltages of each battery are equal, then the voltage leaving the junction would be equal to the voltage of each battery. This means that whether we had one 12-V battery or five 12-V batteries in parallel, the voltage for the entire circuit is still 12 V. According to Ohms law, the product of total current and equivalent resistance would equal 12 either way. So, adding a second battery (of identical voltage to the first) in parallel would not change the overall current in the circuit. It would make the circuit run longer though. It would be like making a galvanic cell with a bigger anode and cathode plates of the same material. The reaction still has the same
emf, but because you have more grams of reactant, it will run longer.
Also, if you keep adding resistor after resitor in parallel, it won't impact the voltage quite as you said. The total current will keep on increasing with each new parallel pathway being added, but it will not overload the battery. It
could overheat the battery and thereby reduce the voltage (current going up would raise the battery temperature) or it could prematurely drain all of its power (run the reaction dry quickly), but in theory, the addition of parallel resistors simply lowers the equivalent resistance of the circuit and thereby raises the total current (current leaving the cathode and arriving at the anode). But, the voltage does not change; it's a property of the battery. It's like kinetics versus thermodynamics. A faster reaction (one with a catalyst for instance) ends sooner, but with the same equilibrium constant and free energy if it's the same reactants.
Hopefully this makes sense.