I'm not quite sure I understand the question, but here is my thought.
The absorbance of DNA with a compound bound to it at any specific wavelength will be a combination of the absorbance of the DNA itself + the absorbance of the compound at that wavelength. The absorbance may not be an exact summation of the two absorbances due to potential electronic interactions between the DNA and compound or to an effect of the compound on the structure of the DNA, but in any case the absorbance will almost certainly be higher than that of the DNA alone.
The challenge here is that if you just add a DNA binding compound to a solution of DNA, some of the compound will bind to the DNA and some will remain in solution, based on the equilibrium of the binding interaction. The free compound will contribute to the overall absorbance. It would be necessary, therefore, to create a situation in which there is a negligible concentration of free compound, by using a very tight-binding compound and a high concentration of DNA relative to the equilibrium binding constant.
I mean , is it possible in the groove binding mode, a ligand cause increase the absorption intensity of DNA? or increase in the absorption intensity of DNA just observe in the intercalative mode? or both?
The UV absorbance of DNA is due to a combination of the UV absorbance of the bases reduced by the hypochromicity that occurs due to base stacking. Anything that disrupts the base stacking will increase the UV absorbance, such as heat denaturation. It's possible that a compound binding in the major or minor groove might affect the base stacking by causing a change in the backbone structure, for example by localized unwinding. I would expect the effect to be quite small, since complete heat denaturation only increases the absorbance by 37%.