Let's start out with an air breathing SSTO, like Skylon. These things have pretty bad mass ratios and pretty razor thin margins. Given that the engines react with the oxygen in the air during the first stage, you'll have an unequal ratio of fuel to oxidizer. The limit of the air breathing stage is dictated by limits of the mach number with the ramjet operation.
But what if you had a crazy scheme to extend this air breathing mode? It's a shorter trip to move air from the upper atmosphere to space than it is from ground to space. Additionally, your fuel tank will be contracting during the air breathing mode. There's extra empty volume in your craft being freed up while at the same time you're swimming in Oxidizer. What if your engines siphoned some extra air into an expanding 3rd tank near the end of your air breathing stage, which is then reacted with the fuel during the first part of your airless flight?
Would you have to use a gaseous form? Or given the cryo temperatures that Skylon has in some parts, could it be possible to liquify some amount of air? Perhaps the heat exchangers can't handle this, so it's completely ridiculous. Nonetheless, if they could, Oxygen liquifies before Nitrogen if I understand correctly, so this could tip the ratio in your favor. If you did use a gaseous form, perhaps this would require hardening the fuel tank, which would kill whatever mass ratio benefit you were hoping for.
Can we manage to rule this out categorically (as in there's no realistic scenario where it helps), or would it only be a matter of vast additional complexity?