There are a few different parts to this question.
Firstly, you cannot file two claims for the same loss at the same time.
You can however, submit a claim for a damaged i-phone for example, and then submit a claim for a stolen laptop (albeit that would be a very unlucky individual indeed!).
You may find that when submitting a claim, you’re often asked if there is another policy of insurance which could cover the losses claimed for. This is because, in the event of a valid claim, your insurers will look to recover a proportion of any sums paid from the other insurance company.