Not strictly, as you would need to build up a 2nd set of no-claims for the second car.
However you could approach your current insurer, explain the situation and they may be be prepared to offer you a couple of years introducory bonus.
Alternatively you could look at a multi-car policy, i've included a link below. These allow you to have more than one car and more than one driver on the same policy, only needing one set of no-claims. But from personal experience is can be cheaper to insure each car separately.
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