The DM is allowed to make any alterations to the game rules that they wish, which includes defining how Magic Items behave. That being said there are the following trends:
The mending cantrip states that it cannot restore magic to a broken magic item. This suggests that destroyed magic items lose their magical powers. So, cutting up a robe or cloak to resize it, is likely to just destroy it.
Magic items like the bag of holding or chime of opening become mundane if they are broken or torn, again suggesting that a destroyed item is always non-magical.
Silver plating an item is usually unnecessary, since magic weapons can hit through almost all resistances, but the weapon isn't necessarily being destroyed, so this is up to DM rule more than anything.
Also, keep in mind that sentient items may not like being modified, and will actively resist attempt to do so. Page 143 of the DMG also lists several minor properties which may impact an item's ability to be dyed or modified.
As far as something simplistic like a dye is concerned, there is nothing in the rules to suggest that painting a +1 shield or dying a Cloak of Protection will cause the magic to become mundane. There is only an implication that breaking, tearing, or destroying the items will make them non-magical. There is some nuance that your DM will have to make the calls on. For example, dying a Cloak of Elvenkind would be a DM call since there is no rule about the matter in the object description.
In most cases, if you aren't destroying an item, you can probably get away with something like paints or dyes or potentially silvering without any effect on the magical properties of the item. The grey area would be somewhere where the change stands in opposition to the properties of the item, and then your DM will need to make the call.