There is no question of forming 4 bonds during oligomerization.
In the Lewis-structure of NO3-
you have an electronic structure with one
N=O bond, relatively stable because in period 2 the pi-pi orbitals do overlap pretty good, for the atoms are small.
In period 3 the atoms have a greater size, so these elements don't form strong double bonds, the P=O in a similar structure as in NO3-
is weak or hardly existing because pi-pi interaction is weak. Thus PO3-
is an unstable species on its own.
easily adds up to PO43-
to form P2
, a more stable dimer with only single P-O bonds. And this can go on with the next PO3-
attaching to form a trimer P3
This explanation disregards p-d orbital interaction in phosphates, but it is of some help. There is a general tendency to form only single bonds in the third (and higher) period, e.g. compare CO2