Talk to your DM
There are no specific rules about armor types being converted from one to another and whether or not this is possible.
The Equipment lists seem to indicate that each one is it's own thing and thus suggests that they aren't additive or reductive in any RAW way.
Whether or not a DM will allow conversions like this, or how they'll make it work if they do, is up to them to decide.
As Illarion says in their answer, there can be unforeseen problems if this is permitted. Combining multiple magical armors is what comes to mind first.
Pieces of Armor
Plate (PHB, 145) is described as:
Plate consists of shaped, interlocking metal plates to cover the entire body. A suit of plate includes gauntlets, heavy leather boots, a visored helmet, and thick layers of padding underneath the armor. Buckles and straps distribute the weight over the body.
If we look at the strict RAW on this, the armor is made up of interlocking metal plates to cover the entire body, but also has some specific parts: gauntlets, boots, and a helmet.
A DM could interpret this to mean that the specific pieces mentioned may be changed out for other magical items (e.g. gauntlets of ogre power, boots of elvenkind, helm of telepathy), but that the remaining armor is a single item that doesn't have interchangeable parts.
However, the language is 'loose' enough that a very strict DM could say that you can't change any of it out.
Ultimately, this is a conversation with your DM about what is reasonable and what is not. But the different armor types do seem to be separate, but that some of the pieces do appear to be interchangeable. The breastplate doesn't seem to be as it's not called out as a separate piece. At my tables, we have allowed armor wearers to substitute magical items like those above (boots, gauntlets, and helmets) to be used. But we have required that wholesale armor changes (chain/leather/plate/half-plate/etc) are fully replaced.