In terms of database design, class design, and many other programming tasks, it is often useful to restrict your concept of numbers to there being only three numbers

That is a good rule of thumb, but it is just a starting point. The real rule is, in my mind, whether a data rule requires it; and if it does, how many. If how many cannot be answered with a specific number, a new (child) table is used for them. Otherwise, same table.

For example, if storing email addresses and one alternate, it may make sense to store both email addresses in the same table. Another example (from my current project), if you have an entity created with up to 12 parts (each part being similar to a level), it is likely better to store the 12 parts in the same table.

Technicalities, perhaps. But, this is what i do for a living.