Agglomerate zksnarks Let a, b be two statements. Given succinct (fixed size) zero-knowledge proofs z(a), z(b) that a, b are true, how easy is it to build z(a AND b)?
One way to do this is to construct two pairing-friendly curves such that the scalar field of the "outer" curve efficiently supports arithmetic for the "inner" curve. Then you can define a circuit for a zk-SNARK over the outer curve, that can verify proofs of a zk-SNARK over the inner curve. This can be done by constructing the outer curve using the Cocks-Pinch method, as in Zexe. In this case you would use an efficient zk-SNARK proving system such as Groth16, to reduce the cost of verifying the inner proofs.

Since I first wrote this answer, another approach has become available using $2$-cycles of non-pairing-friendly curves, as in Halo. (I'm a codesigner of Halo, with Sean Bowe and Jack Grigg.)

The #zcash-wizards channel of the Zcash community chat is a good place to ask about such things.

(This answer previously included a suggestion to use a nested pair of curves with the inner curve as BLS12 and the outer curve as BN. In fact there's no known method of matching up the base field of the BLS12 curve with the scalar field of the BN curve, and there are good reasons to believe that it is not possible to do so.)

Note that any of these approaches will only pay off if the number of proofs being aggregated is large.