This is a very elegant study; it is very well controlled and written. There are some few points that authors have to clarify:

Main: In order to use multifocal stimulation, authors adopted the ALE analysis and an average map for a functional connectivity analysis as they refer to the Fischer et al study (2017). Whereas I am totally supportive to the developing of such a new method that aims to better deliver a focal stimulation, it looks a bit odd the choice of the stimulation electrodes in the current multifocal approach:

a)For the mftDCS, the configuration appear to be a circular anode-cathode alternation along all the cortex (in the Fisher study the focus was on the motor areas) likely that every anode and cathode may result to close to each other by running the risk of a potential increase of current shunting over the cranium (e.g. Moliadze et al., 2010) likely reducing the amount of current going through the scalp under the stimulating electrodes. However, authors found the strongest effect by using mftDCS, thereby I am wondering if this may be due by a general enhancement effect from all the cortex (taking into account that the electrodes are all around the cortex) rather than from specific effects generated by the model template.

b)For the mftACS, still here the electrodes configuration appears to be difficult to understand: anterior in at 0 while posterior opposite at 180°. While evidence shows that a parieto-frontal newtwork phase-stimulation modulates WM respect to an anti-phase stimulation(Polania et al.,2012), here authors proceeded to stimulate all prefrontal and parietal (left and right hemisphere)area at 0 and 180°. Despite authors already discussed the possible limitation of the current montage, is there any evidence of a similar network configuration by using tACS? Is it possible that the lack of effect could be due by an interference effect due to the montage and the electrical current flowing in different phase between prefrontal and parietal?

-Most of the tDCS studies showed prominent effects on cortical excitability by offline stimulation. Here it appears that stimulation was delivered online at the onset of every training session. How authors reconcile their online tDCS effects within the framework of plasticity changes that seem to occur when stimulation is delivered online? I would suggest to mention it inside the discussion.

-Authors used a network-like-model for stimulation (multiple brain areas), is that correct to infer that they stimulated both the hemispheres? Since the amount of studies on WM and EF are showing lateralization effects, did authors take into account this issue? In the conventional tDCS protocol the anode was placed on the left PFC, thereby it is unclear if they were hypothesis driven or not. I would suggest to clarify this in the introduction.

Minor: - Page 5 line 7 to 11, authors describe effects of different TES (tACS, tRNS etc..) on cortical excitability and plasticity. Some of these effects are also frequency specific but especially state-dependent (Feurra et al. 2013) due to the peculiarity of the waveforms of the electric fields. This should be mentioned.

• "Five subjects were excluded from the analysis due to non-compliance with the test administration on at least two independent measures." This is very general, were the subjects uncomfortable with stimulation or for example they did not complete the training etc…?

• Gender of subjects: what was the percentage of males and females ? It looks no clear.

• As reported above, while I am supportive of networking stimulation, I would suggest the authors to better clarify in the discussion that despite a functional connectivity model for stimulation may have resulted in robust effects (e.g. mftDCS), these novel models seem to be very far from the classic (bipolar) and most recent HD montage (ring-like montage). I believe that a simple clarification and suggestion could be very useful to those who use these techniques in different branches of research such as psychology and clinical neurology.