I'd like to purchase a Lamy with three converters and fill them with different inks all at once. This way I can swap converters and use a different ink every day. Is this possible or practical?
No problems with your process. The only drawback is the residual ink left in the nib. If you go from black to blue, the ink will look black until you get blue ink to the nib. Minor issue though.
You are going to need to flush the pens in between, some say that mixing inks, especially different brands can sometimes hurt the pen. Something about ph levels and acidity I think. Also, if you leave a converter open to the air, I don't know how long it will take to dry out.
Not saying not to try it, someone else may have already. As with everything YMMV.
+1 on pretty much everything Dave said above. You would definitely need to flush, particularly if you are mixing inks between manufacturers. Different formulations can cause sometimes harmful chemical reactions that can cause sediment, clogging and other issues. You will also have drying issues with the open converters.
You will have problems with residual ink in the nib, especially when going from dark to light, or end up "mixing" colours ... blue to red or red to blue will give you purple, &c. Maybe you are fine with this 'gradual shifting'.
You will potentially have problems if the old and new inks are not chemically compatible. There could be a reaction that turns the ink to goo inside your nib/feed.
You still need to flush out the nib occasionally as part of regular maintenance.
Why not just get a few pens and keep them all inked up, and switch back and forth ... better than if you are on "red ink" day and all of a sudden you need blue ... or vice versa.
I sort of did this at one point by swapping converters between two Pilot 78Gs, or maybe it was a 78G and a Plumix. The gradual change in ink color on each was interesting. I don't remember what the inks were, but at the time I think I had almost all Noodler's. The main point was to try the different inks with the different nibs in the two pens.
If I were keeping a converter outside of a pen, but already inked, I might be able to improvise a cover for it, but it would probably also be a good idea to stand it up somehow so it wouldn't leak. Really seems like more trouble than it would be worth. Personally, I've taken the more expensive, but for me more enjoyable route of having a wide variety of pens. At the moment I can lay my hands on pens with blue, purple, black, green, brown, and grey inks in them.
You're going to want to clean the old ink out of the nib/feed so you might as well dump any remaining ink (what, two or three drops) back into the bottle, rinse out the converter and start fresh.
That said, I've had a few half filled carts standing up in a bottle top on my desk before. I put a small piece of tape over the end to avoid evaporation.
Flush well. And when you think you have flushed enough, flush a bit more. I converted my Al-Star from a Baystate Blue pen to a Lamy Black (I ordered it just for the bottle). I have had no problems, and BSB supposedly can cause some problems if not cleaned out thoroughly.
Oh, and to those who know my love of BSB- I still have it in my Studio.