I am studying photoelectric effect and it is known that if the irradiated light on metal surface has a lower frequency than that of work function the electrons do not eacape, no matter how intense the light is. However, I imagined a thought experiment where work function is W=hυ and light consisting of photon with a frequency υ/2 is irradiated on the metal surface. Suppose the electron absorbs 2 (or more than 2) photons of energy hυ/2 each. It then has an energy equal to (or greater than) the work function and hence can escape the surface. Then we have a case where electrons are knocked out by light of lower frequency than the work function. In a similar way, we can have an electron knocked out of the metal surface by light of lower frequency but sufficient intensity so that there are many photons which the electron can absorb to gain enough energy to escape. Why can't we have this situation?
Multi-photon ionisation is possible, but the probability of it occurring is very low unless extremely strong fields are applied. But it was definitely a topic of interest in the 1960s: see for example this article deriving the expression for the rates, this article observing it in Cs$_3$Sb. For whatever reason interest seemed to wane after the 1960s, but recently with the increased accessibility of strong field sources there has been somewhat of a revival of interest in multi photon processes such as this. See for example these slides for a nice overview
Usually this is not possible. As described in the comments, a photon can be absorbed when an atom has two energy levels, and the photon contains just enough energy to promote an electron from one to the other.
Another way a photon can be absorbed is if it contains so much energy that the electron escapes entirely from the atom. In that case, any (high) photon energy will do. The extra energy goes into the kinetic energy of the photon plus recoil of the atom.
But there are special cases where two (or more) photons can be absorbed in two separate steps. This is sometimes taken advantage of in lasers to double or triple the frequency of light. If there are two sets of energy levels with just the right separation, a photon can promote an electron to one higher energy, and the second can promote it again. See this article on Upconversion.
Another way involves crystals with nonlinear response to electromagnetic waves. In a classical picture, electromagnetic waves exert forces on electrons, making them oscillate. Usually atoms are like springs. $F = kx$. Double the force to double the amplitude. But in some crystals there is a quadratic term. $F = k_1x + k_2x^2$. See Nonlinear Index.
This can cause higher frequencies to be emitted. Some lasers take advantage of this to emit higher frequency light. The non-linear component is usually weak. It takes a very intense light to excite it. These lasers often concentrate a lot of energy in a very short pulse. See this article on Frequency Doubling.