Yes you can with a smart strategy.
It's possible the impression share loss due to rank includes losing out on impressions that the campaign is eligible for but are very broad so you would not want to show for them anyway.
Start new campaigns with a manual bidding strategy until the algorithm has enough data to switch to automatic. Then, see how high you can push the algorithm to automatically raise its goal (i.e. target CPC of $X could be the goal). You must have conversion tracking set up correctly before running any campaigns or else you will be feeding the wrong data into the machine learning algorithms, which will obstruct its ability to get results. You can check this by going to the Conversions report and checking the “Include in Conversions?” column and making sure that only the appropriate conversion actions are included.