Right/left align lines after the first one inside multline and across (math mode)

Question

I have an external align environment and the computations inside each line are longer than the available width, so I wrapped each of those inside a multlined environment. Inside each of these multlined environments I'd like to right align (or left align with an additional indentation with respect to the first line) the lines following the first one. How can I achieve it?

Here is an example of what I have so far and I need the three lines that I marked with % at the end to be all right aligned (or left aligned with an addition indentation with respect to the main line).

\phi(asdfg) &= \phi(asd asd asd asd asd asd asd asd asd)\\
            &= \begin{multlined}[t]
                   (fgh fgh fgh fgh fgh fgh fgh fgh) (fghfghfgh) \cdot \\
                   \cdot (fghfghfghfghfghfghfghfghfgh)^{-1} (asd) %
               \end{multlined}\\
            &= \begin{multlined}[t]
                (qwe qwe qwe qwe qwe)(qweqweqwe)(qweqwe)^{-1} \cdot \\
                \cdot (asdasdasd asdasdasd) (asdasdas) (asdasdadasd) \cdot\\%
                \cdot (asdasdasdasdasd) %
               \end{multlined}\\
            &= \begin{multlined}[t]
                ...and so on...
               \end{multlined}
\end{align*}            

UPDATE (after @Bernard's answer):

To clarify my question here is a picture of what I need.

Any other suggestion on how to nicely typeset the above computations is more than welcome!

Answer 1

If I've well understood what you want, you simply can use aligned in the place of multlined, without any ampersand:

\documentclass{article}%
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{mathtools}

\begin{document}

\begin{align*}\phi(asdfg) &= \phi(asd asd asd asd asd asd asd asd asd)\\
        &= \begin{aligned}[t]
               (fgh fgh fgh fgh fgh fgh fgh fgh) (fghfghfgh) \cdot{}  \\
               {} \cdot (fghfghfghfghfghfghfghfghfgh)^{-1} (asd) %
           \end{aligned}\\
        &= \begin{aligned}[t]
            (qwe qwe qwe qwe qwe)(qweqweqwe)(qweqwe)^{-1} \cdot{} \\
            {} \cdot (asdasdasd asdasdasd) (asdasdas) (asdasdadasd) \cdot\\%
            \cdot (asdasdasdasdasd) %
           \end{aligned}\\
        &= \begin{aligned}[t]
           \textit{ ...and so on...}
           \end{aligned}
\end{align*}

\end{document} 

Unless you mean this: