Actually I'm not sure what can be done. Both OG's and my (pipe-dream) suggestion probably fail because a large proportion of the public might not really care. To persuade such people that (a) politics matters in their daily lives, and therefore (b) they should participate in it, is a huge struggle that won't be overcome either just by offering another choice -- that anyway would be drowned out in parliament -- or by reforming politics to make each vote genuinely matter.
Still, it's notable that in the EU referendum, or the Scottish independence Referendum, turnout was massively boosted from typical general/local elections. Both referenda, of course, had a simple "most votes nationally wins" system, between two choices. Perhaps you can at least persuade *some* more people to vote if the electoral system feels more competitive, so that one person's vote does start to matter more, but I'm not going to pretend that it's a complete solution.