In general, BET is applicable to low pressure range, not necessarily the monolayer adsorption range.
According to BET theory, it is not necessary to have a fully formed first layer for the second to start forming; this is a good assumption and it is indeed what occurs in real cases. Although most of the adsorption will occur on the solid surface before monolayer formation, there is a statistical probability of molecules adsorbing on top of the incomplete monolayer. This is especially true when the C value of the BET equation is less than 2 (where it starts to look like a type III isotherm).
However, the BET derivation does have assumptions that occur at low pressures: the most critical one being that there is no lateral interaction between adsorbed molecules. If you plot the isotherms in the BET-linearized fashion (that is, $\frac{p/p^0}{n(1-p/p^0)}$ as a function of $p/p^0$) you will see that the values deviate from linearity at pressures above $0.1-0.3$.
The best way of selecting the correct range for fitting the BET plot, is the classic paper by Rouquerol:
Rouquerol, J.; Llewellyn, P. L.; Rouquerol, F. Is the BET Equation Applicable to Microporous Adsorbents? In Characterization of porous solids VII; Studies in surface science and catalysis; Elsevier, 2007; pp 49–56.
