Yeah definitely. I've experimented with a number of more 'interesting' mechanics as rewards for the breakpoints. Ultimately, they all, much like the current stat-y one, created a feeling in the player of "but why do I have to wait?" Basically, when you get a tool that alters the way you approach your core combat pattern, the kit feels incomplete without it. The healing on E is kind of cool and adds some decisions, but none that really change the way you approach combat, except that now you are kind of just stronger.
As a comparison point, consider Syndra. Her ability augments don't really change the way the abilities function. They just sort of add some power (increased damage, increased slow duration, etc.). The one that really stands out to me is the increased cast range on the ultimate. Cast ranges are pretty sacred as far as I've learned. Opponents learn approximately what your threat range is and then play around it, so when that changes things get really whacky. I think it's okay for Syndra since nobody really learns to play around the range of the ultimate, as it only happens once per fight and often within the range of her other abiltites. But when you do this for Noxious Blast or Twin Fang or other abilities that are nearly always up and core parts of a Champion's threat, things start to break down. There are champions who are all-about increasing threat range, like Kog'Maw and Tristana, but that aspect is core to the champion identity, so players learn to play around it.
As a point of contrast, consider Kha'Zix. His W, E, and R change pretty dramatically when they're evolved. It's pretty important here to nail down the differences between Kha'Zix and Cassiopeia. What is it about Kha'Zix's abilities, which dramatically change his threat ranges and counterplay, that doesn't leave the Kha'Zix player feeling like she's missing something when she doesn't have them? Is it something about the evolution system, or the individual abilities themselves? I think it's pretty clear that it's the evolution system, but what about it? I think a lot of it has to do with it being a core part of the champion's identity, that both kha'zix players and opponents know going into a game that that's his thing. But it doesn't end there. I think the choice there and the reliability is really important. Kha'Zix (and Victor also) can choose to get their preferred upgrade about as early as they can want it. The augmentation of abilities is much more in the hand of the players in these cases (and even to Syndra) and so it doesn't feel like the game is witholding a core ability for them, but rather they get to upgrade their champion how/when they want to. That's the prevailing theory anyway.
So, the question is, what sorts of things make sense to come over game time in ways which you can't control super well? One answer is 'just make it an evolution system like Kha'Zix/Victor,' but I think that design space is starting to get a bit crowded and it's really important that we preserve what makes those champions feel unique. Stats sort of work, but they create a similar feeling of the game playing keep-away with your power. Somehow the Twin Fang augment works, as it's power in a way which adds some softer decisions and doen't really change Cassiopeia's combat pattern. So, if we're going to swap out the stats for more interesting things that feel exciting to get rather than necessary, it would have to fit along these lines.
Sorry for the rant, hope that helps!
Stashu, why does Cassiopeia need to feel like she's randomly gaining power uncontrollably? From a lore standpoint, she betrayed Sivir, got bit by a snake trap, and ended up being transformed into a gorgon. Unless she's going Akira on us, she should be at the peak of her potential.
Cassiopeia first and foremost is a spy. Not the kind like her sister, mind you, but a more out in the open spy. She seduces, she deals in secrets, and returns those secrets to her country for the glory of her house. Her new VO is nothing but her talking about how secrets are worth more than gold. So unless she eats secrets like magical wheaties, it makes no sense to have her be focused on being a hyper carry AP mage who ramps up power. She operates from the back lines, spreading venom, lies, poison, and deceit. Therefore, her focus should be her poisons and not her E. Her passive should not be this power gaining stack system, as it does not fit with her characterization at all.
First off, drop Aspect and give her a new, more fitting passive. Maybe something simple like a poison amp aura that increases the damage of her poison the closer she is to the foes. If not that, have it be a conditional buff regarding her poisons. I don't know, but the possibilities are endless and they all can create a fluid ability that isn't what she has now.
Secondly, if you're concerned with her laning, find a way to give her a weakness that doesn't involve completely crippling her kit if she misses a skillshot. Personally, I thought her extreme lack of mobility and short range in her old kit was a comparable weakness, but hey, clearly I don't know how to balance videogames like you do.
And finally, as everyone else has said before, change the focus on her kit. E was never a focus and should never be a focus. We like Cassiopeia because she is so far one of the rare few mages who expressly deal in . All your rework and dumping all into E does is make her a conditional burst mage. We want DoT (which stands for Damage Over Time), not burst. Again, DoT, not burst. An E-centered Cassiopeia is burst, because her current "DoT" is nothing more than a set up for burst. So lose this focus and give the power back to her DoT. DoT has it's counters, on account of it not killing immediately and giving more time to react via potions or life steal, so if you figure out how to balance DoTs and reinfuse her kit with it as a focus, you will have earned our favor.