Supose I have a diameter duration version of veil of invisibility. I am roaming the castle of a noble and find myself in a tight spot: I am in the middle of a hall and my diameter duiration spell is about to end in 20 seconds. In that moment a few guards enter the room from different directions. Can I recast the spell (quietly) BEFORE it ends, so they do not see me for an other diameter duration? Or would I need to have the spell end before recasting it on myself?
Take a rebellious grog. Magus A turns him into a rat for day duration. Then Maga B decides that rat is too good for him and turns him into a woodlouse. Then Magus A and Maga B cannot agree to disagree and change him back and forth. It's the same situation, isn't it? Otherwise you could protect somebody from being turned into somebody else by casting a spell on him. The only question is:
does your spell have to penetrate your old spell?
pro: It makes recasting more unstable (which creates tension).
contra: My slothful nature feels repulsed by thinking about all the extra work this would be for a player.
I see no reason why you cannot cast it again. Furthermore, in the specific case of veil of invisibility, you could have two active at the same time - they wouldn't benefit you any more than a single one, but you wouldn't need to beat the previous casting total: if the species are destroyed by one spell, they are destroyed just as well by two.
Of course you can. The only prohibition is that spells do not add to each other.
Let's take a different example. Let's give it Sun duration.
You are about to go against a hedgewizard that you know can dispel Imagonem effects. So, you cast it, say, 20 times on yourself. You now have 20 identical invisibility spells running. All 20 of them would have to be dispelled to reveal you.