Does the word "that" give a possibility to simplify a Past Perfect sentence?

I'm talking about the past and then I make a digression farther to the past and start adding had before every verb. And I want to say this:

There had not been many people that had been disappointed with their assignments.

There had not been many people that were disappointed with their assignments.

Which way to say that is correct? Does the first verb perhaps establish the tense and after that you can take a more simple way to say it?

Answer

Just to provide context, let's define your past as something like,

Sartorius took over the department in March.

That gives you a Reference Time. Now you want to use a past perfect to look back to the time leading up to his appointment:

[At that time] there had not been many people that had been disappointed with their assignments.

But in the real world, writers don't allow themselves to get trapped in this sort of unnecessarily complex construction; they junk the sentence and rewrite:

At that time few people had been disappointed with their assignments.

And you don't even need that past perfect. You can accomplish the same thing unambiguously with a simple past and an adverb:

Before that, few people were disappointed with their assignments.

Keep FumbleFingers' Perfect Truism in mind:

Don’t use Past Perfect unless you really have to.