Dear Prof. Deshpande,
What I observed with the few Brāhmaṇas of Maharashtra that learned more than one Veda is that they usually affiliate to the first Veda they learned as their svaśākhā (which should be the Veda of their family, thus determined by birth, although this is often not the case). The additional Vedas learned after their own Veda (usually portions thereof or the Saṃhitā of the next Veda at the most) are usually considered secondary. In some cases the second Veda learned is more important for their ritual activities. For example I witnessed that some Yajurvedins had learned the Sāmaveda and thus were known and hired often for their expertise in chanting the second Veda (as there are fewer Sāmavedins in Maharashtra), yet still considered Taittirīya their svaśākhā and Āpastambha or Hiraṇyakeśī their Sūtra.
I hope this anecdotal information helps. If I remember correctly Scharfe in his Education in Ancient India (2002) collected some of the textual references on the rules of first learning one's svaśākhā and then proceeding to the next Veda, but unfortunately, I do not have the book at hand right now.
Best,
Borayin Larios