To expand on Tohsters answer, one hamburger menu is already detrimental enough so adding a second one is only going to confuse matters more.
If the client cannot be persuaded to follow other avenues then it's probably best to start looking at ways to make the best of a bad situation. (this blog post expands on this https://lmjabreu.com/post/why-and-how-to-avoid-hamburger-menus/)
Adding "menu" next to the hamburger. This can increase user
interaction but does not fix the problems with the menu itself.The
following give some numbers in the increase in interaction.
Summary : Adding menu to the hamburger, or just simply menu on it's own increases click rate. An example of this is an image taken from exisweb.It's not a huge difference but it's enough to convince you that simply adding menu will increase interaction.
Tab bar or side bar. I would say at the minute for a resource heavy
site with a lot of content a sidebar is the best option at the
minute, whereas a tab bar with limited menu options is by far the
best option for a forward facing site where you need to instantly
show the user your most important features quickly and obviously. (http://kong.vn/ios-navigation/)
The aspects to take into consideration are :
Taking into account of these, Tab bar can be much more beneficial in all aspects except space taken, in which it will always be a fixed element on your page (otherwise it'll just be another side bar!). Not to say side bar doesn't have it's place as if you have a lot of content and actions, they have to be displayed somehow.
I would give more links but my reputation currently prevents me from doing so, this is something I did some research on before but I was still not able to get enough solid evidence to move away from a hamburger menu for our mobile site at the minute.
You are the professional in this situation so it's your job to do your best to convince him this isn't the smartest avenue to go down, alternatively if this is just one job and not a repeat task it might be easier to grit your teeth and split the content on each side with one hamburger menu.