Is Photoelectric Effect continuous or discrete? I don't understand how electrons and photon interact with each other when a metal surface is illuminated with light. I've read that below a certain threshold frequency or wavelength of light, no matter how much we increase the intensity or time of exposure, no electrons get emitted because the photons don't have sufficient energy and assuming that only one photon interacts with one electron. It is considered to be discrete rather than continuous. But i think it could be continuous. 
Let's consider a photon of red light whose wavelength is above the threshold wavelength (i.e insufficient energy to emit electron). Let this red photon hit an electron. The electron just goes to higher energy level but is not freed since energy required is less. Now since the electron remains in higher energy level for some time, it has high chance that it gets hit by another photon of red light since the speed of light is very high. The same electron can be hit by the next photon since the time next photon arrives is very very less than electrons transition time. So can't the electron in higher level get the energy of 2nd photon and travel to next higher level before it goes to ground level and so on it can be freed from the atom?
 A: What you are describing might be possible - that a series of interactions with photons might cause an electron to first be excited, and then to be emitted.
However, the probability of an individual electron interacting with two photons in quick succession without an intermediate interaction with other electrons (and thus an opportunity to shed the excess energy) is effectively tiny. Macroscopically speaking, if the flux of incident photons was really this high, then the material would increase in temperature, the electron motion would increase, and the probability (Boltzmann statistics) of an electron escaping would indeed go up.
But that would no longer be the photoelectric effect. It would be called "heating". As @garyp points out in his answer (and Jon Custer in a comment to this question) a highly focused and intense laser beam can be (and has been) used to do "two step" excitation of electrons, demonstrating that the effect you were searching for does indeed exist in nature.
A: This is possible, and it's done.  It's used as a form of spectroscopy.   It's called two-photon photoemission.    See, for example this.
A: electron can't escape  from atom in your case, why because if electron is at energy level say E1 (got it from photon of light) and another photon colloide it, then electron can have energy to take transition from E0 energy level to E1(if electron is at E0 level), in this case electron is at E1 enegy level so it requires E2-E1 amount of energy to take transition from E1 to E2.
