The conformation of single-chain nanoparticles (SCNPs) in the presence of linear polystyrene crowding molecules has been studied by small angle neutron scattering under contrast-matching of the crowders. A model describing the scattering of aggregating polydisperse SCNPs has been developed, resulting in the determination of the potentially squeezed size of the individual SCNPs within aggregates, their local chain statistics, and the average aggregation number, as a function of crowding. Two different crowders, of low and high molecular weights, are shown to have a different effect: while long chains tend to impede their aggregation above their overlap concentration, short ones are found to mediate depletion interactions leading to aggregation. Self-imposed crowding within the aggregates has a similar impact on chain conformation independently of the crowding of the surrounding medium. Our results are compared to recent simulations and shall contribute to the microscopic understanding of the phase behavior of soft intrinsically disordered nano-objects and in particular the effect of crowding on biomacromolecules.