Men with multiple wives are often accused by other Christians of being 'covetous' and filled with 'lust' as though these were sins. In using these words they display their ignorance of Scripture. It is not a sin to covet or lust - it is only a sin to lust and covet something that isn't rightfully yours.
The trouble is the English language has evolved (even if Yahweh's marriage laws haven't). These days the words 'covet' and 'lust' have an exclusively negative meaning, which causes problems for those reading the old King James Version (KJV) of the Bible which uses these words differently from today. Modern versions use words like 'desire' or 'eagerly desire' which is what the words 'covet' and 'lust' used to mean. Thus it is, in modern English, to 'eagerly desire' a woman with a view to marrying her, is acceptable, but if you 'lusted' after her you would be considered a sexual pervert. Thus from the point of view of old English it is perfectly acceptable to lust after a single woman whereas to lust after a married one is an abomination. The words 'covet' and 'lust' are morally neutral words in KJV English.
Is it wrong or a sin for a single woman to desire, eagerly desire, covet or lust to be a part of a family where there is already one or more wives? No, it is not. Is it wrong or a sin for a married man to desire, eagerly desire, covet or lust after a single woman to make her his wife? No, it is not. [N.B. I hereby state that anyone wishing to quote this paragraph must quote the two paragraphs above as well so as not to distort the meaning of what I am saying]. But if he is a righteous man, walking in Yahweh's commandments and seeking to please Yah'shua (Jesus) his Messiah (Christ) he will, of course, not only be obedient to Yahweh's wishes in the matter (Yahweh may say 'no') but also be sensitive to his existing wives' concerns before taking another wife. He will be a Christian gentleman.
Finally, if he is under a monogamy-only covenant with his first wife, the husband cannot unilaterally break it without becoming a vow-breaker, which Yahweh views as a serious sin. Considering almost all contemporary Christian men and women marry with this exclusion clause in their vows ('no other' means precisely that), then unless his wife agrees, without being under any sort of duress, to release her husband from his monogamy-only vow, he may not covet, lust, or eagerly desire another single woman. He has bound himself over to being monogamous and must remain so even if, had he known the truth about plural marriage, he would never have entered such a contract in the first place. There are two parties to any contract and his wife entered the marriage vows with the express understanding that he would be a lifelong monogamist. Whilst he can, should, and must be true to the Bible teaching on the subject of plural marriage once he has discovered it, he must also not cast a desirous eye on any unmarried woman as a man who honours his word and his vows. If he does, he is untrustworthy and unworthy of the trust his first wife would have to give him should she agree to anull the monogamy-only part of their vows so that he can bring another wife into the family. The men of plural marriage must be honourable and trustworthy. If they are not, then they become just another class of scoundrel.