This Vim plugin provides text objects for chain members: im and am. It depends on the textobj-user plugin.

There is no established terminology, so I made one up. You know method chaining as in foo.bar().baz(), right? A member chain is an abstraction of that, because such a chain could also consist of attributes, fields, properties, however you want to call variables of a class. A chain member then is just a member in a member chain. Easy. :)

Why not just use targets.vim's i. and a.? Let me show a few examples, in the fantastic notation of that plugin.

For am, the first chain member includes the dot to its right:

cursor position │ .....
buffer line     │ first.second.third
selection       │ └ am ┘

..., all following members the one to their left:

     .......
first.second.third
     └ am ─┘

im does not include the dot:

     .......
first.second.third
      └ im ┘

Method calls can be selected outside their argument list:

     ........          .
first.second(arg1, arg2).third
     └────── am ───────┘

Dots and other special characters inside the argument list are skipped:

     ........               .
first.second(arg1.var, foo()).third
     └───────── am ─────────┘

Inside the argument list, the outside is ignored:

             ......
first.second(foobar.var, arg2).third
             └ am ─┘

Chars and string contents are ignored:

     ........         .
first.second(") ", '.').third
     └────── am ──────┘

Type parameters are no problem, either:

     ........              ...
first.second<Type.InnerType>().third
     └────────── am ─────────┘

..., nor are (multi-dimensional) arrays:

     ........         .. .
first.second[foo.index][j].third
     └─────── am ────────┘

... and curried function calls:

     ........       ..          .
first.second(foo.bar)(foobar.baz).third
     └─────────── am ───────────┘

More than one member can be selected:

.....
first.second.third
└── 2im ───┘

..., or the next or last one:

.....
first.second.third
     └ anm ┘
            ......
first.second.third
     └ alm ┘

..., which can be combined with a count:

.....
first.second.third
     └── 2anm ───┘

So it turns out that these text objects are also pretty handy to select all sorts of function calls and accesses by index. However, there are a few things that fall inside undefined behavior. Consult :help textobj-chainmember-limitations for more information.