You could do this by some sneaky border code stuff which threw away the given path (which is a box around each subpage) and drew just the bottom line for the relevant pages but I don't think that would look all that great since the lines wouldn't join up and wouldn't be vertically centred (as the pages are slightly shrunken).
So here's an alternative which defines a "background" page which is put behind all the others and which takes up the whole page. On this we draw three horizontal lines. This is never written to by the pgfpages page collection mechanism and is copied from (physical) page to (physical) page. The only downside is that if you have a total of 17 slides then the second physical page (which has only one logical page) still has all three lines drawn on it.
Here's the code:
\documentclass[xcolor=dvipsnames, handout]{beamer}
\usepackage{pgfpages}
\usepackage{pgffor}
\beamertemplatenavigationsymbolsempty
\pgfpagesdeclarelayout{16 on 1 with background}
{
\edef\pgfpageoptionheight{\the\paperheight}
\edef\pgfpageoptionwidth{\the\paperwidth}
\edef\pgfpageoptionborder{0pt}
}
{
\pgfpagesphysicalpageoptions
{%
logical pages=17,%
physical height=\pgfpageoptionheight,%
physical width=\pgfpageoptionwidth,%
first logical shipout=2,%
}
\pgfpageslogicalpageoptions{1}
{%
resized width=\pgfphysicalwidth,%
resized height=\pgfphysicalheight,%
center=\pgfpoint{.5\pgfphysicalwidth}{.5\pgfphysicalheight},%
border code={%
\pgfusepath{discard}%
\pgfpathmoveto{\pgfpoint{0pt}{.25\ht0}}%
\pgfpathlineto{\pgfpoint{\wd0}{.25\ht0}}%
\pgfpathmoveto{\pgfpoint{0pt}{.5\ht0}}%
\pgfpathlineto{\pgfpoint{\wd0}{.5\ht0}}%
\pgfpathmoveto{\pgfpoint{0pt}{.75\ht0}}%
\pgfpathlineto{\pgfpoint{\wd0}{.75\ht0}}%
\pgfusepath{stroke}%
},%
copy from=1,%
}%
\pgfpageslogicalpageoptions{2}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.125\pgfphysicalwidth}{.875\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{3}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.375\pgfphysicalwidth}{.875\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{4}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.625\pgfphysicalwidth}{.875\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{5}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.875\pgfphysicalwidth}{.875\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{6}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.125\pgfphysicalwidth}{.625\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{7}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.375\pgfphysicalwidth}{.625\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{8}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.625\pgfphysicalwidth}{.625\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{9}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.875\pgfphysicalwidth}{.625\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{10}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.125\pgfphysicalwidth}{.375\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{11}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.375\pgfphysicalwidth}{.375\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{12}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.625\pgfphysicalwidth}{.375\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{13}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.875\pgfphysicalwidth}{.375\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{14}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.125\pgfphysicalwidth}{.125\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{15}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.375\pgfphysicalwidth}{.125\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{16}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.625\pgfphysicalwidth}{.125\pgfphysicalheight}%
}%
\pgfpageslogicalpageoptions{17}
{%
border shrink=\pgfpageoptionborder,%
resized width=.25\pgfphysicalwidth,%
resized height=.25\pgfphysicalheight,%
center=\pgfpoint{.875\pgfphysicalwidth}{.125\pgfphysicalheight}%
}%
}
\pgfpagesuselayout{16 on 1 with background}[a0paper,border shrink=5mm, landscape]
\begin{document}
\begin{frame}[plain]
\titlepage
\end{frame}
\foreach \k in {1,...,31} {
\begin{frame}{Frame \k}
This is frame \k
\end{frame}
}
\end{document}
Result:
I'm not sure if an answer is still of interest. Anyway:
1) I would strongly advise to use the pdfx package:
\usepackage[a-1b]{pdfx}
2) The error in the pdfx package is caused by the way how the timestamp is put together. Depending on your timezone (e.g. UTC+1, UTC-1, etc) you have a different sign there. This causes the issue.
Use of \getTZh doesn't match its definition.
You therefore need to put the pdfx.sty in your working directory and need to adjust that specific line accordingly:
\def\getTZh +#1#2{\edef\xTZh{#1#2}\getTZm} % change - to + if error occurs (due to timezone)
...
T\xHour:\xMin:\xSec+\xTZh:\xTZm}} % change - to + if error occurs (due to timezone)
Alternatively, you may change the timezone of your system.
3) pdfx automatically loads the hyperref package, too. If you want to have a customized hyperref setup, you can use:
\hypersetup{
unicode,
colorlinks=true
}
In addition to that, you need to provide a color profile and a valid xmp file. Information on this can be found in the pdfx manual. This solution relies on pdftex.
I'm not aware of any solution using dvips.
Best Answer
Looks like no, unless someone has a fix the author isn't aware of. From the Beamer manual, section 4.6.2 (Printing the Handout):