The Fallout wiki has an extensive list of known Vaults, as well as their purpose. Each vault description is backed by in-game material you are suppose to look for, but it does appear to confirm that there are no other vaults to be found as of yet.

• Vault 75: Vault 75 is an experiment in improving the human genome. It appears these tests were carried out using selective breeding, genetic modification and hormonal treatment. The test subjects have their growth accelerated, and at 18, are "disposed of". It is suggested that in certain situations, such as for the purpose of replacing research staff, exceptional candidates may have been used for other means.

• Vault 81: Vault 81 is a testing facility involving antibodies, disease and radiation. Vault 81 was under express orders to not evacuate under any circumstances, unless an official "all clear" was issued. In the event of an evacuation, it is suggested that the overseer would order the 'dweller section' to be mass-incinerated, including the dwellers.

• Vault 95: Vault 95 is a social experiment on isolation and drug addiction. All dwellers were drug addicts, and the experiment started pre-war.

• Vault 111: This is the vault our hero comes from, and was a test in cryogenics and long-term suspended animation.

• Vault 114: Vault 114 was another social experiment, where the inhabitants consisted almost entirely of upper-class society. The living conditions of the vault was advertised as highly luxorous, but in reality, it was the exact opposite. The overseer was chosen from the general population, and the interview process favored qualities such as no leadership skill and issues with authority. The purpose is listed in a terminal; "By taking away the luxury and authority these groups saw in surface life, we hope to study their reactions in stressful situations."

In researching the related question How can I break items down into their components, I saw a complaint on Reddit to the effect that the extra, leftover materials get destroyed.

Why this is a common belief

Many people seem to believe this, and there's a good reason for that: it's confusing. And it's confusing for two reasons:

1. The composite item is removed from your character's inventory, but the leftover components are placed in the Workshop's inventory.
2. There's sometimes a delay before the leftover components reappear. If you want to speed up the process: go into Workshop mode, try to build something, and then exit. This appears to force the Workshop to update its inventory contents list.

Go, science!

I settled the question with science. I've tested this with various items a dozen or so times using the Armor Workbench, the Weapons Workbench, and the Workshop crafting menu.

The leftover components have always (so far) appeared in the Workshop inventory, but there's sometimes a delay.

Here's one of the experiments:

Experiment

• Remove all Lead from your inventory and the Workshop's inventory.
• Add two pencils to your inventory; each pencil has 1 Lead and 1 Wood.
• Go into the Wood Structure crafting menu—not to craft anything but just to check your Wood component count.
• Craft a Radiation Emitter, which among other things requires 2 Lead.

By creating the Emitter, we force the Workbench to dismantle the pencils, which liberates 2 Wood and 2 Lead.

If our Wood component count goes down, wood has been lost/destroyed. If it stays the same, our 2 "potential" units of Wood have simply been converted into 2 actual units of Wood.

Result

Our Wood component count remains unchanged. So unneeded materials are retained, just as though you'd broken the item down yourself.