Can the Past Continuous be used for future events?

I am taking Spanish classes next week.

Despite that it is Present Continuous, it tells us about the future. But if I put it to the past, will it retain its meaning?

That day I started new life. I was taking Spanish classes next week.

Answer

In non-formal conversation this is fine, except it needs more articles:

a new life, because you are not starting new-life-in-general but a particular (albeit unspecified) new life, which presumably you are going to describe.

the next week, because bare next week always means 'next' with respect to the time when you are speaking.

It's barely acceptable in formal use, too; but as a matter of courtesy to your readers it is desirable to pin down your time references a little more precisely. Otherwise readers will see was taking and assume that it refers to that day, and then have to revise that interpretation when they come to the next week. Write this instead:

That day I started a new life. I would be taking Spanish classes the next week, and &c

Effective communication is driven by the principal of minimal effort; but that means very different things in written and spoken English, because the two media present radically different constraints:

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  Written English is governed by The Adamantine Law: Whatever can be misunderstood will be.

  
  

  When you write you have no opportunity to correct your readers' misunderstandings. Consequently you must take care to express your thoughts as clearly and unambiguously as possible, so no misunderstandings arise. It is your reader's effort which must be minimized, not your own.

  
  


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  Spoken English, in contrast, is governed by The Tolerance Maxim: Whatever should be understood may be omitted.

  
  
  

  When you speak you are engaged in a conversation. You and your interlocutors share extensive knowledge of the situation which need not be specified, you may speak elliptically and allusively in confidence that your interlocutors will fill in the holes and tacitly ignore or adjust any syntactical or grammatical blunders you commit. If significant misunderstandings arise, they may be corrected. All parties share the effort.