Expand after all that stuff?

This is provided by etextools as \expandnext:

\usepackage{etextools}
\expandnext{\somecommand{Some Argument}}{\secondarg}

But if you only like to expand the second argument once you can use a double argument swapping, a trick I use in some of my packages:

\documentclass{article}
%% Implementation
\def\myswap#1#2{#2{#1}}

\def\expandafterallthat#1#2{%
    \expandafter\myswap\expandafter{#2}{#1}%
}
%%%%%%%%%%%%%%%%

% Test case:
%
\makeatletter
\def\somecommand#1#2{%
    \def\first{#1}%
    \@onelevel@sanitize\first
    \par\texttt{First argument: \first}%
    \def\second{#2}%
    \@onelevel@sanitize\second
    \par\texttt{Second argument: \second}%
}
\makeatother

\def\secondarg{\empty Some stuff\empty}

\begin{document}

\expandafterallthat{\somecommand{\empty Some Argument\empty}}{\secondarg}

\end{document}

This correctly prints: (the \emptys are to see if the argument got expanded further)

first argument: \empty Some Argument\empty
Second argument: \empty Some stuff\empty

Written without a package

\documentclass{article}
\newcommand\expandafterallthat[2]{%
  \expandafter\expandafterallthataux\expandafter{\romannumeral -`0#2 }{#1}%
}
\newcommand\expandafterallthataux[2]{#2{#1}}
\newcommand\somecommand[2]{\detokenize{#1:::#2}}
\newcommand\secondarg{\thirdarg}
\newcommand\thirdarg{\fourtharg}
\newcommand\fourtharg{example}
\begin{document}
\expandafterallthat{\somecommand{Some Argument}}{\secondarg}

\end{document}

will multiply-expand input. (You don't say whether to expand #2 once or several times.)

---

With the latest engine releases (MiKTeX or upcoming TL'19), one can use \expanded:

\documentclass{article}
\newcommand\expandafterallthat[2]{%
  \expanded{\unexpanded{#1}{#2}}}
\newcommand\somecommand[2]{\detokenize{#1:::#2}}
\newcommand\secondarg{\thirdarg}
\newcommand\thirdarg{\fourtharg}
\newcommand\fourtharg{example}
\begin{document}
\expandafterallthat{\somecommand{Some Argument}}{\secondarg}
\end{document}

(\expanded has always been in LuaTeX, so you can test there even without the latest updated engines.)

Since Joseph did not mention expl3 yet, let me do that: the LaTeX3 bundle includes a module for expansion control, l3expan. In particular, this includes functions to expand arguments of a command, of the form \exp_args:N... where the dots are letters corresponding to how the various arguments should be treated.

Many letters are in use: n for a brace group which should be passed with no modification, o to expand once, f to expand fully from the left, stopping at the first non-expandable token, x to expand fully throughout, like in an \edef. There is also N for a single non-braced token which should be passed as is, c for text that should be made into a control sequence, then treated as an N argument, and V and v for variables (see the l3expan documentation for details).

Here, you want to expand the second argument once, and leave the first unchanged, so the variant you need is \exp_args:Nno: leave the function unchanged (N), the first argument, braced, unchanged (n), and the second expanded once (o).

\newcommand{\foo}[2]{\showtokens{#1... #2}}
\newcommand{\sometext}{Some text.}
\RequirePackage{expl3}
\ExplSyntaxOn
\exp_args:Nno \foo {\error} {\sometext}
\ExplSyntaxOff