Basically, the multi-propose Approval Voting we recently used, is designed precisely for that. Approve an alternative means approval, no vote to an alternative means oppose. The result gives that or those alternatives which have highest net voter number, just as Irpen wishes with "approve & oppose". The only basic structural weakness of Approval Voting (if voters are honest) actually is that it is not designed to register priority order of a voter and thus not whether an individual approve vote is strong or weak. But even this can be made by enlightened voters, they just need to write "weak approve" or "strong approve" when voting for any alternative - and the interpretation will be the task of the interpreter. However, what happened with the (yet ongoing) vote is not due to weaknesses of the voting system, but due to the problem that our subject is difficult to name in a generally accepted way. She simply is difficult. There are reasonable, sufficiently-well-founded arguments her to be placed under headings which almost all make some to oppose. And thus the vote splits. This being the basic situation, NO VOTING SYSTEM will ever cure it - unless using "violence". Of course a voting system could be designed which favors something and violates some others, and thus a decision will be made - against half of the population who are then totally pissed at. Such voting systems were used by dictators, by oligarchs, etc.
Personally, I am somewhat puzzled why not a higher number of people came and put their (perhaps secondary, or label "weak") approval to "Alexandra of Hesse" - but that is the result of the will of those voters.