The Freundlich isotherm was the first isotherm model proposed for sorption processes. It can be applied for non ideal sorption on heterogeneous surfaces, as well as, multilayer sorption.
The possible exception would be Langmuir, since it described a chemisorption process due to the saturation of the sites. This can be overcome if the surface is a micropore where a saturation point exists. However, this approach would be physically incorrect.
The first thing is whether it is adsorption or adsorption. Second is the phase of adsorption. Is it between L-G or S-L or S-G. Only on those you can decide which isotherm is applicable
The Freundlich eq. can only be applied for monolayer type adsorption and it is specifically suited for heterogeneous surfaces and low adsorption values (far away from surface saturation).
The Langmuir eq. is limited to a monolayer, this also implies that the concentration or pressure range is restricted to not too high conc (sufficiently below solubility)./rel. pressure, but the surface saturation is accounted for.
The BET eq. allows for multilayer adsorption. Mostly it is used for gas adsorption and is applied up to intermediate relative pressures.
For typical multilayer adsorption up to high relative pressures the Frenkel- Halsey-Hill eq. for gas adsorption is more appropriate.
Shah is correct, multilayer adsorption is physisorption and in the BET model it is a kind of condensation. But physisorption may also occur in a monolayer so it is not restricted to multilayer adsorption. Chemisorption is restricted to direct contact with the surface and therefore to monolayer adsorption.
Recently I had the opportunity to study the paper:
M. Muttakin, S. Mitra, K. Thu, K. Ito and B. Baran Sah. Theoretical framework to evaluate minimum desorption temperature for IUPAC classified adsorption isotherms. International Journal of Heat and Mass Transfer 122 (2018) 795–805. https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.107
which may contain valuable information about your question. On the other hand, there is always the possibility that you can develop your own model.
first you can use any model to describe your results and all models you mentioned will be represent your results but one of them identical more than others with your results and then you can know this model by using statistical indicators and finally described the adsorption based on the model.
Physisorption is due to the operation of forces between the solid surface and the adsorbate molecules that are similar to van der Waals forces between molecules. The adsorption increases rapidly at high relative pressure, finally leading to condensation on the surface. At high relative pressures, even before condensation occurs, there may be several superimposed layers (multilayers) of adsorbate on the surface. So Langmuir well describes multilayer adsorption better than Freundlich which better describes strong adsorption which mainly monolayer.
Any of the four isotherms could be physical adsorption . Chemical adsorption involves the formation of new covalent bonds comparable to that between two combining atoms and such process are characterized by high enthalpy of adsorption, usually more than 10 times the value of about 20 kJ / mole characteristically observed for physical adsorption. The main difference between the four isotherms rest on the basis of the assumptions used in deriving each of them or the manner in which the equilibrium concentration affect the amount of adsobate per unit mass of adsorbent. While Freundlich is purely empirical, Langmuir assumes that the adsorbed molecules form a monolayer, which do not interact with one another and that the enthalpy of adsorption is independent of surface coverage. However, BET assumes multilayer coverage of the adsorbent or substrate by the adsorbate. It may also be valid to make similar assumption for Kisliuk isotherm. None of the isotherms models is gauged by the strength of bond between the adsonbent and adsorbate, therefore depending on the strength of bond, any of them could be physical of chemical. It may therefore be essential to determine the strength of the bond from the temperature dependence of the interaction. This will help in determine whether the equilibrium is physical or chemical.