that's an interesting technical question. Normally a covalent single bond where both electrons in the bonding electron pair come from one atom is called a coordinate covalent bond. Typical examples are the ammonium ion (NH4+), formed from NH3 and H+, the hydronium ion (H3O+), formed from H2O and H+, and the prototypical BF3 adducts BF3(NH3) and BF3(OEt2) (OEt2 = diethyl ether). In all cases the bonding elecron pair comes from the N or O atom. A covalently bonded oxygen atom has two lone-pairs of electrons. However, in simple molecular compounds it can form only one coordinate covalent bond which creates a positive charge on the resulting ion. I assume that a second coordinate covalent bond will cause a strong repulsion so that the second electrophile will not form a bond. Moreover, the remaining lone-pair is much less nucleophilic. That's certainly the reason why ions / compounds like H4O2+ and Et2O(BF3)2 do not exist.
Thank you very much for your interesting question. I think, Dr. Frank T. Edelmann has already posted a good answer to this question. An atom, molecule or ion may act as ligand if (i) it has a filled octet along with at least one lone pair electrons, and (ii) it should be sufficiently nucleophilic. After forming a coordinate bond, the ligand becomes positively charged as stated by Frank T. Edelmann . So the resulting system has less tendency to donate the second electron pair forming a second coordinate bond. Therefore I think, the presence of lone pair electrons on a species is not the only condition to act as ligand. As an example, I would like to talk about formation of nitric acid molecule. In the HNO2, one lone pair electron is present on the nitrogen atom and the octet about the N atom is fulfilled. On the other hand, O atom has only six electrons (equivalent to three lone pairs) in its valence shell. However, coordinate bond is formed between HNO2 and O atom where, the O atom is an electron pair acceptor although it has three lone pair electrons !
To my knowledge, it is not so uncommon that a single atom would share more than one electron pair to form coordinate bonds. For example, halide ligands can involve their lone pairs to form two or three bonds with different metal centers acting as bridging ligands, for example see Inorg. Chem. 2015, 54, 8, 4076–4093