The etymology of this suffix is given at length by the OED -
Etymology: In Old English *-sciepe, -skiepe (rare), -scipe, -scype, Anglian -scip, (occas. -sciop) strong masculine = Old Frisian
-skipi , -skip, -schip (West Frisian -skip , -schip, North Frisian -skep, -skap), Old Saxon -scepi , -scipi , Middle Low German, Middle Dutch -sc(h)ip, -sc(h)êpe, -sc(h)eep, -sc(h)êp, West Flemish
-schip, -schepe < Germanic *skapi-z, < skap- to create, ordain, appoint (see shape v.). The ĭ of the stem-syllable of Old English
scipe and the corresponding continental forms is apparently due to
secondary influence of the umlaut, the change being probably favoured
by the lack of stress. The related *skapo-z (masculine), *skapō
(feminine), and *skapti-z shaft n.1, meaning ‘creation, creature,
constitution, condition’, were used in Germanic as the second element
of compounds and as such assumed the function and meaning of a suffix
equivalent to *skapi-z; these forms are represented by Old Saxon -skap
(Middle Dutch, Dutch -schap), Old High German -scaf (feminine), later
-scaft (Middle High German, German -schaft), Old Norse -skapr (Danish -skab, Swedish -skap); the alleged Old English landsceap is an error due to misreading. The abnormal forms of the suffix in Scots
hussyskap, -skep, -skip (see housewifeship n.) may have a Low
German or Dutch origin.
The important part of that is perhaps the meanings of creation, creature, constitution, condition.
Five separate nuanced senses are given but they are all clearly related, meaning the state or condition of being. Examples of each vary from 1.adjectival, DRUNKENSHIP, HARDSHIP, WORSHIP 2. added to nouns FRIENDSHIP, LORDSHIP 3. Designating person of rank REEVESHIP 4. State of life, occupation or behaviour CLERKSHIP, COURTSHIP, 5. Added to nouns forming compounds TOWNSHIP (this is the only modern example given, and I don't fully understand the distinction from 2.)
I am not sure if this answers the question, but it does provide some etymology, and the manner in which the suffix is used. Further words I feel sure could be created if they fell within one of those categories, and there are plenty more in everyday use e.g. ACQUAINTENCESHIP. But how about DRIVERSHIP e.g He handed over to another member of the party the drivership of the vehicle?