The problem of solving sequences of linear systems is a key issue in many optimization techniques. Recently, in the iterative solution of large-scale systems there has been a growing interest in improving the solution of the overall sequence by sharing some computational effort throughout the sequence. To this end, cheap updates of an existing preconditioner for one matrix of the sequence have been proposed in order to build preconditioners for subsequent matrices. In this talk we address the problem of solving sequences of KKT systems arising in large-scale optimization methods for quadratic programming and focus on Constraint Preconditioners (CPs). Though CPs are very effective in the iterative solution of KKT systems, their setup may still account for a significant part of the computational cost of the optimization procedure, thus motivating the interest towards cheaper CP approximations. We discuss some techniques to build approximate CPs for KKT sequences arising in interior point methods for quadratic programming, through low-cost updates of a seed CP preconditioner. Both updates and low-rank corrections of the factorization of the seed preconditioner are considered. Numerical results showing the performance of these techniques are presented.