How do I slightly change amplitude of the 230 VAC loaded power line?
Point number one. You seem to want to work with mains connections. Know what you're doing, take all necessary precautions. Don't kill yourself, and then try to sue me for giving you this information.

For a very small voltage change, the simplest is to use an auto transformer.

Let's assume that you want to be able to change up to 10 volts at 20Amps. Although your total throughput is 20Amps x 240v = 4800 watts, the power required for the transformer is just 10 x 20 = 200 watts.

If the variation you need is fixed, you can simply buy a mains transformer with the required power and secondary voltages. Say you bought a 200VA mains transformer with two 5v 20A secondary windings. You would then be able to vary your mains voltage by putting one or both secondaries in series with the incoming mains, using the appropriate phasing to either increase or decrease the voltage by 5v or 10v.

If you want continuous variation, then there are three options.

a) Buy a 200VA transformer kit, which has the mains winding already done, and wind your own custom secondary, suitable for 20A, with as many taps as you need, one per turn if you like!

b) Buy a 20A Variac. This would be very big and heavy, but would give you continuous variation from 0v to a little above mains voltage.

c) Buy a 1A variac, and the 10v output 200VA transformer. The 1A variac is much smaller and cheaper than the 20A version. Power the input of the transformer from the output of the variac. The transformer output will now give you continuous variation of 0v to 10v and a current capacity of 20A. Connect with the appropriate phasing to increase or decrease the mains voltage.

Note, strictly speaking, the 10v mains transformer I have described is not an auto-transformer, but an 'ordinary' transformer. However, with the connection I have described, it does function as an autotransformer. At this high ratio, there is practically no copper to be saved in making parts of the windings common.