Comprehensive understanding and possible control of parametric instabilities in the context of inertial confinement fusion (ICF) remains a challenging task. The details of the absorption processes and the detrimental effects of hot electrons on the implosion process require as much effort on the experimental side as on the theoretical and simulation side. This paper describes a proposal for experimental studies on nonlinear interaction of intense laser pulses with a high-temperature plasma under conditions corresponding to direct-drive ICF schemes. We propose to develop a platform for laser-plasma interaction studies based on foam targets. Parametric instabilities are sensitive to the bulk plasma temperature and the density scale length. Foam targets are sufficiently flexible to allow control of these parameters. However, investigations conducted on small laser facilities cannot be extrapolated in a reliable way to real fusion conditions. It is therefore necessary to perform experiments at a multi-kilojoule energy level on medium-scale facilities such as OMEGA or SG-III. An example of two-plasmon decay instability excited in the interaction of two laser beams is considered.