We prove that all lattices of \(\text {Sp}(2n,\mathbb {R})\) , except those commensurable with \(\text {Sp}(4k+2,\mathbb {Z})\) when \(n=2k+1\) , contain the image of infinitely many mapping class group orbits of Zariski-dense maximal representation that are continuous deformations of maximal diagonal representations. In particular, we show that \(\text {Sp}(4k,\mathbb {Z})\) contain Zariski-dense surface subgroups for all \(k\ge 1\) .
