There is no standard limit on the output of SHAKE256. No matter what output size you use, SHAKE256 advertises collision, preimage, and second-preimage resistance up to a 256-bit security level against a classical adversary, and up to a 128-bit security level against a quantum adversary, limited by the size of the output for small outputs (see Table 4 in Appendix A of the SHA-3 standard for details).
In particular, you are not limited to a 1600-bit output. SHAKE256-$d$ does not simply reveal up to $d$ bits of the state and stop at 1600. Rather, it reveals up to 1088 bits of the 1600-bit state, then permutes the state, and repeats until it has produced $d$ bits. In spongy lexicon, it repeatedly squeezes up to 1088 bits at a time out of the sponge after absorbing the input. It leaves 512 bits of the state secret at each iteration, far more than an adversary could ever hope to find even with a quantum computer.