The thing is, Narrow Pass in no way implies that you get any "additional" summons on top of your Normal Summon. It says "Both players can only Normal Summon up to 2 additional monsters on their sides of the field."
This is very clear text. Special permission to summon additional monsters would not be phrased this way, as the phrase "you can only" is, as Fury implied, a restriction and not a bonus. If an effect says "you can only activate this effect once per turn" we know it's a restriction on the number of time you could ordinarily activate an effect. If an effect says "you can only equip this card to a monster on your side of the field", then we know its a restriction on what would normally be a legal target for an Equip Card. If an effect says "you can only activate this effect during your Standby Phase", then we know that this is a restriction on the timing of when the card the normally be activated, even if the effect could not normally be activated during a Standby Phase, it's still a restriction because it cannot be activated at its normal time.
Narrow Pass says "Both players can only Normal Summon up to 2 additional monsters on their sides of the field." So that is a restriction on the number of times you could ordinarily Normal Summon a monster. Bot notice in every case, the key phrase to remember is "what you could normally do." It's a restriction on what you can normally do. No additional permission is granted in the text to do anything outside of the normal rules of gameplay.
This reminds me a fellow at Pojo, who insisted that because the text on Dimension Wall stated "you can only activate this card when your opponent declares an attack with a monster.", that because you cannot attack with anything but a monster card, then the phrase "attack with a monster" must mean "in battle with another monster and therefore, cannot be activated against a direct attack. His logic was "well, what else can you attack with? A Spell Card?" He didn't understand that "attack with a monster" means just that, and didn't imply any additions or subtractions.