Accepting that objective morality and individual property rights are true, that is, they are accurate and valid, one can therefore make the case that collective property rights are true.
Put simply, each individual has an exclusive claim (or right) to their body. Their consciousness, an effect of the body, is in control of the various voluntary functions of that body. Since individuals external to the body cannot make such a claim without performative contradiction, each individual's claim is exclusive. Logically, if an individual has an exclusive claim to their body, they also have an exclusive claim to the effects of their body. Such effects include their life and liberty. A subset of one's life and liberty is labour, the application of one's time, effort, and talents on the physical world. When an individual uses their labour to transform an unclaimed object they mix a part of their life and liberty with that object. The object in question therefore can be exclusively claimed by the individual. Such a claim creates a condition of ownership, whereby an object external to one's body becomes property. This is the basis of individual property rights.
Property can be used as the owner desires. It can also be traded to other individuals, a process of abandoning one's exclusive claim while simultaneously assigning it to the other party and receiving the other party's property in exchange. Gifting is another use of property whereby one abandon's their exclusive claim by assigning it to another individual without receiving anything in exchange. One can also simply abandon their exclusive claim outright without assigning it to another party, leaving it open for another to claim.
If an individual can simultaneously (and voluntarily) abandon their exclusive claim and assign it to another individual through the act of trading or gifting, or abandon their exclusive claim altogether, they can also assign their exclusive claim to other individuals while simultaneously holding a share of that exclusive claim. This act of inclusion might coincide with an exchange of value with the prospective party contributing something to the owner in exchange for assignment of partial ownership, or it might simply involve the owner assigning partial ownership as a gift to the prospective party. It is worth mentioning that collective property does not necessarily need to begin as individual ownership, as two or more individuals may labour on an unowned object and agree to share ownership of the new property.
There is no reason to suggest that an exclusive claim must always be limited to a single individual. Exclusivity simply means excluding others from a claim, it does not specify that others cannot be assigned a portion of that claim by the owner.1 The size of each share might be equally distributed amongst the owners or some other arrangement might be preferred. For those who have socialist2 economic preferences, such arrangements might be called a commune. For those who have capitalist2 economic preferences, such arrangements might be called a company. There may even be those interested in pursuing meritocratic arrangements.3 For the sake of brevity, the specifics of such arrangements will not be discussed here.
At all times each individual reserves the right to divest themselves of their share of the collectivised exclusive claim to property. If they voluntarily entered into the sharing of property, they must also be able to voluntarily abandon their share. Such an abandonment might entail receiving compensation equal to the value of the share they are divesting themselves of (an exchange or trade), or it might entail total abandonment (gifting their share to another individual or leaving their abandoned claim open for another to claim in their stead).
At no point does collective property imply nor justify statist ownership as a collective property right, otherwise known as "public property". While monopoly governments may claim ownership over the territory they occupy, that does not mean their claim is valid. History shows that governments were not formed through voluntary means, but rather through coercive means (which clearly invalidates their claim to collective property). Even if, for the sake of argument, such claims were somehow valid, they would be invalidated by the fact that individuals are not free to divest themselves of their share of the collective property. If individuals were free then there would be no imposition of compulsory payments (taxation) to fund the maintenance and protection of the property. An individual who does not acquiesce to the demands of monopoly government will find themselves either kidnapped (arrested and imprisoned) or murdered4 for daring to resist the state's invalid claims.
To summarise, property can be claimed by a single individual and later assigned to other individuals to form collective property. Property can also claimed by a collective from its inception. The formation and dissolution of collective property necessarily rests on voluntary and mutual agreement between individuals. The share of collective property that each individual owns can be equal, based on merit, or based on some other arrangement. Individuals are free to divest themselves of collective property. Monopoly governments, or states, do not have a valid claim to collective property ("public property") as individuals are not free to divest themselves.