In this work, a novel superimposed pilot scheme, named superimposed cross-pilots, is proposed for fractional parameter estimation in multi-antenna orthogonal time frequency space (OTFS) receivers. Assuming a large uniform linear array (ULA) size at the receiver, the multipath components are separated in the angular domain through a matched filter (MF). It is then shown that the proposed superimposed pilot scheme enables the computation of integrated delay and Doppler profiles by averaging the received delay-Doppler matrix across the Doppler and delay axes, respectively. This procedure helps reduce data-to-pilot interference via data averaging, eliminating the need for iterative cancellation schemes. Based on this, a fractional parameter estimation algorithm, which exploits MFs, is derived. Simulation results show that the proposed approach outperforms existing OTFS superimposed pilot schemes, achieving a lower bit error rate (BER) while exhibiting a trade-off between peak-to-average power ratio (PAPR) and communication performance.