It is clear from the end of the Pasuk (verse) “V’chol Asher L’reecha” (nor any thing that is thy neighbor’s - Shmot 20, 14) that the prohibition to covet applies to everything and is not limited to the things stated in the Pasuk.
The Torah deliberately chose the order: house, wife, slave & maid, Shor (ox) & Chamor (donkey), in order to teach us the desired mode of behavior that the wise people will first buy a house then a wife then a slave & maid, and a ox & donkey to plow his field. In Mishneh Torah (Devarim 5, 17) the wife is mentioned first because the young men have a desire to first get married and then get a house or because coveting a wife is the bigger sin among them.
[אבן עזרא בהקדמה לעשרת הדברות שמות כ א, ורמב"ן שמות כ יג].
The expression “Shor V’Chamor” usually symbolizes any animal not specifically a Shor or a Chamor, we find this expression in many Mitzvot:
In the prohibition of Lo Tachmod – “Lo Tachmod Beit Reiacha Lo Tachmod Eishet Reiachah V’avdo V’amato V’shoro V’chamoro V’chol Asher L’reecha” (Thou shalt not covet thy neighbor’s house; thou shalt not covet thy neighbor’s wife, nor his slave, nor his maid, nor his ox, nor his donkey, nor any thing that is thy neighbor’s - Shmot 20, 14).
In the Law of pit damage – “V’chi Yiftach Ish Bor O Ki Yichreh Ish Bor V’lo Yechasenu V’nafal Shamah Shor O Chamor” (And if a man shall open a pit, or if a man shall dig a pit and not cover it, and an ox or an donkey fall therein - Shmot 21, 33).
In the Mitzvah of Hashavat Aveidah (returning a lost item) – “Ki Tifga Shor Oyivcha O Chamoro Toeh, Hashev Teshivenu Lo” (If thou meet thine enemy's ox or his donkey going astray, thou shalt surely bring it back to him - Shmot 23, 4).
In the Mitzvah of Shabbat – “U’vayom Hashvi’I Tishbot Lema’an Yanuach Shorcha V’chamorcha” (but on the seventh day thou shalt rest; that thine ox and thine donkey may have rest - Shmot 23, 12) “V’yom Hashvi’i Shabbat L’Hashem Elokecha, Lo Taaseh Kol Melachah, Atah Uvincha Uvitecha V’avdecha V’amatecha, V’shorcha V’chamorcha V’chol Behemtecha” (but the seventh day is a Sabbath unto the LORD thy God, in it thou shalt not do any manner of work, thou, nor thy son, nor thy daughter, nor thy slave, nor thy maid, nor thine ox, nor thine donkey , nor any of thy cattle - Devarim 5, 14).
In the prohibition of Kilayim – “Lo Tachrosh B’shor Uve’chamor Yachdav” (Thou shalt not plow with an ox and a donkey together - Devarim 22, 10).
In the prohibition of Chasimah – “Lo Tachsom Shor B’disho” (Thou shalt not muzzle the ox when he treadeth out the corn - Devarim 25, 4).
The Mishnah in Bava Kama explains that the reason that Shor & Chamor are commonly used, is because the Torah talks about what’s commonly used, and the ox & donkey are commonly used, a ox for working in the field and a donkey for carrying loads.
The Gemara says that it seems to people that Lo Tachmod is only without money(ב"מ ה:), meaning that people misunderstand and think that only if he does not pay for the object he commits Lo Tachmod, but if he pays money for the object he covets, then he is not committing Lo Tachmod. Nevertheless, the truth is, that he is committing Lo Tachmod when he pays for the object.
It says in Mechilta Derashbi, Lo Tachmod and in the following it says Lo Titaveh (neither shalt thou desire - Devarim 5, 18) to make one guilty for desire in itself and for covet in itself. From where do we know that if one desires he will end up coveting, because it says Lo Titaveh and Lo Tachmod. From where do we know that if one covets he will end up robbing because it says V’chamdu Sadot V’gazalu (And they covet fields, and rob them – Michah 2, 2). Desire is in the heart, as it says Ki Te’aveh Nafshecha (because your soul desires – Devarim 12, 20). And covet is in action, as it says Lo Tachmod Kesef V’Zahav Aleihem V’Lakachta Lach (thou shalt not covet the silver or the gold that is on them, nor take it unto thee – Devarim 7, 25).
[גירסא זו של המכילתא מובאית בספר מקורי הרמב"ם לרמ"מ כשר עמוד צח אות מה, ובספר המצוות לרמב"ם מצוה רסו, ודומה לזה בחומש תורה תמימה שמות כ יד].
According to the Gemara and Mechilta it is ruled in the Rambam and Shulchan Aruch: One who covets his neighbors slave or maid or house or vessels or something that he can purchase from him, and then he sends to him many friends and he pleads of him persistently to sell it to him until he finally purchases it from him, is committing Lo Tachmod.
One who desires his friends house or wife or vessels etc. once he thought in his heart how to buy this thing and he is tempted in his heart to do so, has committed the Lo Taaseh (a negative commandment) of Lo Titaveh, for Taavah (desire) is only in the heart.
Desire leads to coveting and coveting leads to robbery. Because if the owners do not want to sell it to him even though he offers a lot of money and pleads persistently with friends, it will lead him to robbery as it says, V’chamdu Batim V’gazalu. And if the owners will resist him in order to save their money or prevent him from robbing it will lead him to bloodshed. Go and learn from Achav & Navot’s incident.
From this one learns that one who desires commits one Lav (a negative commandment) and one who buys something he desired through pleading from the owner persistently, commits two Lav’s. Regarding this it says “Lo Tachmod” and “Lo Titaveh”. And if he robs he commits three Lav’s.
[רמב"ם פ"א מהלכות גזלה ואבדה הלכה ט – יב, שולחן ערוך חו"מ סימן שנט סעיף י - יב].