Two modal verbs in one sentence?

Question

Wir sollten nicht nur andere, sondern auch uns selbst täuschen können

Why "können" comes at the end of the sentence?
Why are there two modal verbs in the sentence?

Answer 1

Compare:

1. Ich kann dich sehen.
   I can see you. = I am able to see you.

Here I say, that I have a certain capability, namely the capability to see you.

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2. Ich sollte dich sehen.
   I should see you.

Here I say, that something should happen that is not happening at this moment.

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3. Ich sollte dich sehen können.
   I should be able to see you.

In this sentence, I say, that I should have a capability, that I don't have now, and this capability is to see you.

Answer 2

Wir sollten nicht nur andere, sondern auch uns selbst täuschen können.

Let's simplify the example:

Wir sollten täuschen können.

We should be able to deceive.

There's no such rule there could be only one modal verb in a sentence. Combinations with können are especially productive:

Er muss das Ding auch fahren können.

He at least has to be able to drive that thing.

Sie darf besser fahren können als er.

She's free to drive better than him.

Es will laufen können.

It wants to be able to run.

Sie mag dieses Instrument spielen können.

She may be able to play this instrument.

Answer 3

There are two modal words in one sentence because there are two clauses, a main clause and a subordinate clause. These two clauses share a common verb phrase, sollte täuschen können, but the two modals are split up. täuschen sollen, and täuschen können in the separate clauses.

"Wir sollten nicht nur andere täuschen ." Here, the verb täuschen is understood from the following, subordinate clause, so it's not repeated.

"Können" comes at the end of the sentence because it is part of a subordinate clause which follows the main clause:

"sondern auch uns selbst täuschen können."

This is a case where you have to read the German (verbs) backward, starting from the end, to get the meaning.