How can you choose variations for several content experiments?

I'm using the Javascript API for Google Analytics Content Experiments and it seems like you have two choices:

1. Run one experiment at a time and have Google assign the variation, which you can get using chooseVariation(), or
2. Run several experiments at a time and assign the variation yourself using setChosenVariation()

(1) lets Google control the number of users assigned to each variation, which I need, but I have several experiments. This seems pretty basic. What am I missing?

I don't think you're missing anything. My understanding is that the GA Experiments API allows you to allocate a visitor to any version of a single A/B/N test with the Choose Variation command :

cxApi.chooseVariation();

However, this function is only available if you specify the experiment ID when loading the api.js on the page.

If what you want to do is to run several A/B tests on one page at the same time, this is really multi-variate testing and unfortunately this is not available 'out-of-the-box' in GA Content Experiments (it used to be available with Google Website Optimizer). You can still 'fake' it using your own bucketing, with code like :

<!-- 1. Load the Content Experiments JavaScript Client -->
<script src="//www.google-analytics.com/cx/api.js"></script>

<!-- 2. See if the visitor has seen an experiment already -->
<script>
// loop through all active experiments server-side. 
cxApi.getChosenVariation(
 $experimentId
 );

<!-- 3. Bucket the visitor if he isn't bucketed already -->
// loop through your live experiments 
  cxApi.setChosenVariation(
    $chosenVariation,             // The index of the variation shown to the visitor
    $experimentId                 // The id of the experiment the user has been exposed to
  );
</script>

You will need to decide whether you want a visitor to only view one experiment at a time or enter multiple experiments concurrently.

The first option is probably more reliable but means you will have to split your visitor in quite a lot of buckets, meaning your tests will take a long time before returning a result.

If you use the second option, you need to be careful : if your experiments are not independent, you won't be able to trust the test results from Google Analytics, as the statistical tests used in the Content Experiments assume independence. Even if your experiments are independent, you'll need to have an equal split among all variation combinations.

I hope that helps !