There is a Michael acceptor in one substrate that could potentially react with amine in the second substrate, how can I block this reaction? is there any blocking group for Michael acceptor.
The aza-Michael is known to proceed more readily (ie, without base catalysis) than the traditional Michael. You can protect the amine with either a base-labile (eg, Fmoc) or acid-labile (eg, Boc) to block its nucleophilicity completely. You can check Greene's Protective Chemistry for countless other amine group protections. Amine protection is the most straightforward strategy, but if this is not an option, it may be possible to suppress the aza-Michael addition via pH and/or temperature. If your reaction tolerates it, you can cool the reaction mixture down. You may also be able to titrate the reaction to a pH that doesn't activate the Michael acceptor but does reduce the nucleophilicity of the amine. Alternatively, solvent choice (aprotic) may help suppress the reaction. Finally, you can consider ways to ensure that your desired reaction can outcompete your unwanted Michael addition. Without knowing the reactions or substrate, however, it's difficult to be more specific. If you can protect the amine, this is the most straightforward and obvious option.
Book Greene's Protective Groups in Organic Synthesis
If you can't block the amine, you can try to react your avid Michael acceptor with a removeable Michael donor, for example thioacetic acid. Then run your reaction and have as the last step, addition of a base stronger than triethylamine (a Hünig's base like N,N-diisopropylethylamine), which should remove it, restoring the double bond. Thiobenzoic acid may also work, and has the advantage of being UV active so you can quantify the formation of the thiobenzoate ester by TLC or HPLC. Then when the protection is completed, you could run the reaction you want, then deprotect with base. The protection-reaction-deprotection could then be performed in one pot. The main downside is the stench of thioacids, but you are probably working in a hood with a good draft and you could prepare for the reaction by setting up a large plastic container as a bleach bath for soaking all your stinky glassware and stir bars etc. prior to cleaning them.
Along the same lines of blocking the Michael acceptor with a dummy Michael donor, you could try good but bulky nucleophiles like benzamidine. Removal could then be done by either base or acid. The problem with offering more suggestions is that you don't show a reaction scheme, so there's no way to tell what dummy acceptor will be most compatible with your chemistry. I also have no references to which to point you. Sorry that's all the help that could be offered.