Always raise plus sign in text

Question

I have a lot of places in my dissertation where the plus sign appears surrounded by capital letters in text, e.g. NNLL+NNLO.
The problem is that by default, the + is aligned so low vertically, that among caps it looks badly aligned.
By playing around with the \raisebox, I found that it looks quite a bit better if raised by 0.25ex, and still looks fine with lowercase letters, even in situations like a+j.
Is there a way to change the default behavior of the plus sign to always appear raised in text?
I don't want to change what happens in the math mode.

I suppose a potential solution might be to globally substitute raw + by \raisebox{0.25ex}{+} (modulo the issue with space swallowing) or to make latex use a different font for rendering the +.
I just don't know if that's even possible.

---

Reporting on what I implemented based on the answers.
Here's the command I came up with that also accounts for bold and allows typesetting of two consecutive raised spaces with \++.

\makeatletter % https://tex.stackexchange.com/a/31660/35990
\newcommand*{\IfbfTF}{% detect bold font
  \ifx\f@series\my@test@bf
    \expandafter\@firstoftwo
  \else
    \expandafter\@secondoftwo
  \fi
}
\newcommand*{\my@test@bf}{bx}
\makeatother

% https://tex.stackexchange.com/a/567256/35990
\newcommand{\textplus}[1][+]{\raisebox{% font-independent height
  \dimexpr(\fontcharht\font`X-\height+\depth)/2\relax
}{\IfbfTF{$\bm{#1}$}{#1}}}

\ExplSyntaxOn
\NewDocumentCommand\+{}{
  \peek_charcode_remove:NTF + {\textplus[++]}{\textplus[+]}
}
\ExplSyntaxOff

\peek_charcode_remove:NTF requires the expl3 package.

Answer 1

I'm not sure that 0.25ex is the right choice: it actually makes the + sign to be slightly higher than a capital letter.

Using different fonts might also make the situation even worse. For instance, with Times you'd get

because here the + sign sits on the baseline. Can we make the raising independent of the font? Yes: a bit of algebra shows that we need to raise the symbol by half the sum of a capital letter, minus the height of + plus the height of +.

Using David's idea:

\newcommand{\+}{%
  \raisebox{\dimexpr(\fontcharht\font`X-\height+\depth)/2\relax}{+}%
}

Here's the output with Times

and with Computer Modern

Here's a visual proof of the statement about the height. The first + is with my definition, the second is raised 0.25ex. Just look at the top, because at the bottom TeX always uses the baseline.

Answer 2

You could make + active and raise itself in text mode and not in math, but something would break, it is quite hard to catch all cases of \dimexpr \parindent + 5pt\relax and ensure you don't add a \raisebox mid-expression.

I would use a new command for it, \+ isn't defined by default so:

\documentclass{article}

\newcommand\+{\raisebox{0.25ex}{+}}
\begin{document}

NNLL+NNLO


NNLL\+NNLO

\end{document}