What a smart mother, to figure out that your daughter needs help with this. It sounds like she has some deep chasm of longing, a feeling that she never gets what she needs. When you describe her requests being made in a voice that's on the edge of a meltdown, it suggests that those feelings come bubbling up whenever she sees someone else get something -- whether that's a kleenex or a cereal refill.
Could this be simple sibling rivalry? Maybe. Or maybe these feelings come from some early experience where she felt un-attended to, somehow. Or maybe there's a general feeling in your home of there not being quite enough? That's true for many families in these uncertain economic times. Unfortunately, all the kleenex and cereal in the world won't fill your daughter's longings, which come from a deeper place.
The question is, how best to help her with this desperation that's driving her demanding behavior and keeping her from feeling content?
I think your intuition to start setting reasonable boundaries and deal with the ensuing meltdowns is exactly right, as long as "dealing with" means helping her process the feelings. Your daughter doesn't want to feel those feelings of deprivation, not surprisingly. They don't feel good! But she needs to feel them, so they'll dissipate and leave her free to enjoy what she has. And she needs to "show" them to you.
Every time these feelings start to come up, her strategy is to keep them at bay with rigid, desperate demands. When you try to meet those demands, the feelings stay in check a bit -- See, she can tell herself, I do have things, I have a kleenex, just like my sister -- but they don't go away. If, instead of giving her the kleenex, you connect with her lovingly and give her the safety to feel those feelings, she'll have a chance to process them and let them out. So you might just say "Oh, Sweetie, your sister sneezed so she needed kleenex...but you didn't sneeze, you don't need a kleenex....You're ok without a kleenex...oh, Sweetheart, I see you're upset....I'm right here...You're safe...You have everything you need...Later you can have as many kleenex as you want...right now you are safe in my arms."
Hold her if you can, or at least stay close. Be prepared for tears, and maybe struggle (which is what fear looks like when it comes up.) If she lashes out, that anger is an attempt to keep the desperate need at bay, so just keep yourself safe and stay compassionate. If you can create enough safety, she'll be able to get past the anger to the desperate need behind it, and "show" you how that feels to her. Stay present, stay compassionate, and keep reassuring her that she is safe, that she has everything she needs, that you are there to take care of her.
I think this approach will work best if you also begin to "play" with this issue in a way that "over-fills" your daughter's needs. In other words, yes, she needs to experience that deep feeling of "never-enough" to move past it. So when you're feeling good and able to be fully present and compassionate with a meltdown, go ahead and set a limit and nurture her through the meltdown. But she also needs to experience "always more than enough is available" to heal.
To do this, I would begin to be playful about her demands. So when she asks for five books, say "Are you sure that's enough? You can have seven if you want...or ten! You tell me how many." When she wants a kleenex, give her as many as she wants. And whenever you give her things, don't to it grudgingly, as if you think she doesn't really need it and should be satisfied with less. Give it happily, with a flourish of great generosity, as if you are convinced that there is always enough (which, of course, there really is -- and which we always want to convey to our children so we don't pass on a poverty mentality.)
Of course, realistically, you can't always give her unlimited amounts of what she requests. That's why I suggest that you think of this satisfying of her every request as a kind of "play." Certainly do some of it as you go through your day -- whenever you know you really aren't up for a meltdown -- but make sure you also set aside some time each day for special time. During special time, you can "play" with "over-filling" her cup in a big way.
Are you doing special time with her? It's the best way to convince kids that there is always enough of what they really need most -- your unconditional, unlimited love. Here's a link about how to do Special Time:
It's terrific that you figured out this was happening and are helping your daughter deal with it while she's still very young. I wish you luck in supporting your daughter through this.