Multiply blend mode making logo hard to export as a SVG

I am trying to import an eps logo into Sketch which is usually straightfworward but it's coming in with hairlines between elements. On investigating the logo I found it is designed using transparency blend mode multiply.

On saving to SVG it looks all the multiply blend modes and looks wrong.

I've looked on other forums and it says to expand the shape and then flatten transparency but this then completely changes the look of the logo.

Is there a way of getting this to work?