In building your secondary characters, a lot depends on how many words you have to work with.
If you're writing 80K words, you're not going to have time to give your secondary characters much attention.
Make sure their role is defined, put 'em in a funny hat so the reader can tell 'em apart, and work on your main plot line.
If you're writing 120K words, you likely need those secondary characters to come up with at least one subplot that is all their own.
This is big character development country here, because you have to motivate action. In this case, at least one secondary character must be as deep, complex, fully-realized and alive as your protag.
OK. Let' say you have 'writing room' enough that you need at least one fully-expanded secondary character.
How do you develop these secondaries?
It's not just a matter of choosing random, interesting aspects of these guys and tossing them into the story.
You pick and choose the aspects of the secondary characters as carefully as a bride chooses the flowers her bridesmaids will carry.
Let me be didactic here (... even though it isn't really this simple and other folks mileage will vary ...)
Every secondary character exists in your story to interact with some aspect of your protagonist.
So the first step in 'unflattening' the secondaries is to determine why they are in the manuscript.
Cuteness? Wisdom? Damsel-in-distress? Validation for the protags values? Antagonist and counterpoint to his values? Reward? Redeemer or redeemed? Comic relief? Threat? Tempter?
(See how each of these possible 'secondary character' aspects exists in terms of what the secondary is to the protagonist?)
Your secondary character is not just a microphone to hold the other half of a dialogor a plot device that gets kidnapped so the hero can be heroic.
Your secondary character allows the protag to express some part of the theme of the story.
Remember how Christopher Smart said cats were instruments for children to learn benevolence upon?
Your secondary character is an instrument for the protag to learn something on or do something with or be something to or avoid something about or validate something from -- and that 'something' is one of the themes of the story.
So when you start 'unflattening' your secondary character, you first decide what he is doing for, with, or to your protag.
Let's say your secondary character is an instrument for the protag to learn benevolence upon. Secondary Character One is the protag's testy, unpleasant, unpredictable Aunt Myrtle, of whom he is very fond. Those are her traits that relate to the protag, and we do not care how Myrtle's sister or bridge group see her or that she grew up in Crete or that she swims laps every morning at the 'Y'.
When we are 'building Myrtle', we consider the character traits that make Myrtle testy, unpleasant, unpredictable, and yet worthy of love
because this is how she 'fits with' the protag.
Where do these traits come from?
How are they related to one another?
How does she express them?
And that is how we unflatten Myrtle.
Adding in memorable idiosyncracies for your secondary is not in any way wrong.
Tell us Myrtle is a gourmet cook if this colorful bit of whimsy comes up.
But mostly we want to look at the set of Myrtle traits that intimately relate to the protagonist's dilemma. This lets us deepen and expand the secondary character in the most useful direction. This provides us with just that list of characteristics most likely to move the action. These are the character traits that slide naturally into the ongoing narrative.
Putting this in (mercifully) brief form --
We expand the secondary character by asking ourselves how she affects our protagonist.
We look at what she is that delights, annoys, frustrates, or challenges him.