I'm in the thick of my third game (first original project) and I've never really had this problem before now: I'm not bored of my current project, I'm actually rather enjoying working on it. But I'm also considering ideas for my next project. I know what I want the game to be and I know what I want it to be about, but the gameplay and the story is still pretty abstract and I enjoy theorizing it and ironing it out.

Here's my question: is it unhealthy or just a bad idea to even think about my next project before the next game is either complete or mostly complete?

It's perfectly fine to gather ideas for future projects in a notebook or something (I do that too). It is also healthy for your current project, because switching to something else and then going back to it will help you look at it from another perspective and maybe help you find issues or ways to improve.

What is not Ok is starting to actually work on a new project or try to implement new ideas into the current design on the fly (feature creep).

Thanks for that, guys. I had a feeling that:

A: It was fine for me to do what I've been doing (putting the ideas into a document as they come to me)

and B: This community would be awesome and supportive. Glad to be apart of it. :)

Yes, it's unhealthy, especially if that's your first project. If you already have a finished previous game and you need to make some updates/patches then it's another story and it should not hinder you. But pursuing another idea, before the current one becomes a reality, is a straight way to dozens/hundreds of unfinished projects.

And no, unfortunatelly I'm not always strong enough to follow my own advice :)

Well, I wouldn't say pursuing. It's totally fine to write down ideas as they come to you so you don't forget when the time comes. But actively not working on your current project to work on another one isn't good.

Brainstorming is fine; I've found it can help me get inspired to translate ideas from the next project into my current one so that A: the system is already in place if I use the same engine and B: it may also work in my current project.

Well, I wouldn't say pursuing. It's totally fine to write down ideas as they come to you so you don't forget when the time comes.

to translate ideas from the next project into my current one

Like that one for example :) Suddenly you start thinking how to make your engine work with your *next* game, instead of thinking how to finish your current game faster. You start improving your engine, make it more flexible and complex, instead of simplifying it and treating as a disposable piece code.

Anyway, such things are best tought on ones own skin :) I really doubt discussing this would convince anyone. The 10th unfinished project is the best teacher in the end :)