The re-entrant phenomenon is studied in the antiferromagnetic Ising model on a square lattice with the bonds decorated with two and three-coupled spin 1/2 variables (dimer and trimer) in two different scenarios. In the first one ferromagnetic competing decorated bonds are anneal diluted in the system. The exact phase diagrams of the critical temperature as a function of the concentration and of the competition parameter are obtained. In contrast to the single spin bond decoration, a double re-entrant behaviour is observed. The bond percolation threshold P_c=(1-1/2)/2 is achieved and it is independent of the decorating variable. In the second scenario the pure axial decorated system is studied. The analytical temperature against competition parameter phase diagram and the specific heat are calculated and discussed. In this latter case multiple re-entrances are observed for a certain range of the competition parameter. The nature of this re-entrant phenomenon is discussed.