© 2020 American Physical Society. The excitation energy of deformed intruder states (specifically the 2p2h bandhead) as a function of proton number Z along N=20 is of interest both in terms of better understanding the evolution of nuclear structure between spherical Ca40 and the Island of Inversion nuclei, and for benchmarking theoretical descriptions in this region. At the center of the N=20 Island of Inversion, the npnh (where n=2,4,6) neutron excitations across a diminished N=20 gap result in deformed and collective ground states, as observed in Mg32. In heavier isotones, npnh excitations do not dominate in the ground states but are present in the relatively low-lying level schemes. With the aim of identifying the expected 2p2h - s1/2+ state in P35, the only N=20 isotone for which the neutron 2p2h excitation bandhead has not yet been identified, the S36(d,He3)P35 reaction has been revisited in inverse kinematics with the HELical Orbit Spectrometer (HELIOS) at the Argonne Tandem Linac Accelerator System (ATLAS). While a candidate state has not been located, an upper limit for the transfer reaction cross section to populate such a configuration within a 2.5 to 3.6 MeV energy range provides a stringent constraint on the wave function compositions in both S36 and P35.