wheezy multiarch: binutils:amd64 conflicts with binutils:i386?

[Tom Roche <Tom_Roche@pobox.com>]

summary: 3 questions:

1. Can one install both `binutils:amd64` and `binutils:i386` on the same device?
2. If one can: how? or, what am I doing wrong?
3. If one cannot: why not?

details:

I need to setup a 32-bit app (don't ask!) on a 64-bit linode with

> $ lsb_release -ds
> Debian GNU/Linux 7.8 (wheezy)
> $ cat /etc/debian_version
> 7.8
> $ uname -rv
> 3.19.1-x86_64-linode53 #1 SMP Tue Mar 10 15:30:28 EDT 2015

> $ dpkg --print-architecture
> amd64
> $ dpkg --print-foreign-architectures
> i386
> $ sudo aptitude update
> ...
> $ sudo aptitude full-upgrade
> ...

> $ aptitude --version
> Thu Apr 23 00:08:02 EDT 2015
> aptitude 0.6.8.2 compiled at Nov  7 2012 07:08:03
> Compiler: g++ 4.7.2
> Compiled against:
>   apt version 4.12.0
>   NCurses version 5.9
>   libsigc++ version: 2.2.10
>   Ept support enabled.
>   Gtk+ support disabled.
>   Qt support disabled.
>
> Current library versions:
>   NCurses version: ncurses 5.9.20110404
>   cwidget version: 0.5.16
>   Apt version: 4.12.0

> $ apt-get --version
> Thu Apr 23 00:08:39 EDT 2015
> apt 0.9.7.9 for amd64 compiled on Oct 17 2014 09:15:56
> Supported modules:
> *Ver: Standard .deb
> *Pkg:  Debian dpkg interface (Priority 30)
>  Pkg:  Debian APT solver interface (Priority -1000)
>  S.L: 'deb' Standard Debian binary tree
>  S.L: 'deb-src' Standard Debian source tree
>  Idx: Debian Source Index
>  Idx: Debian Package Index
>  Idx: Debian Translation Index
>  Idx: Debian dpkg status file
>  Idx: EDSP scenario file

Among other packages, I need to install `binutils:i386`. However, I can't seem to install that and keep the native/64-bit `binutils`:

> $ date ; sudo apt-get install binutils:i386
> Thu Apr 23 00:08:50 EDT 2015
> Reading package lists... Done
> Building dependency tree       
> Reading state information... Done
> The following extra packages will be installed:
>   libstdc++6:i386 zlib1g:i386
> Suggested packages:
>   binutils-doc:i386
> The following packages will be REMOVED:
>   binutils
> The following NEW packages will be installed:
>   binutils:i386 libstdc++6:i386 zlib1g:i386
> 0 upgraded, 3 newly installed, 1 to remove and 0 not upgraded.
> Need to get 4,993 kB of archives.
> After this operation, 325 kB disk space will be freed.
> Do you want to continue [Y/n]? ^C

> $ date ; sudo aptitude -s install binutils:i386
> Thu Apr 23 00:08:21 EDT 2015
> The following NEW packages will be installed:
>   binutils:i386{b} libstdc++6:i386{a} zlib1g:i386{a} 
> 0 packages upgraded, 3 newly installed, 0 to remove and 0 not upgraded.
> Need to get 4,993 kB of archives. After unpacking 14.7 MB will be used.
> The following packages have unmet dependencies:
>  binutils : Conflicts: binutils:i386 but 2.22-8+deb7u2 is to be installed.
>  binutils:i386 : Conflicts: binutils but 2.22-8+deb7u2 is installed.
> The following actions will resolve these dependencies:
>
>      Remove the following packages:
> 1)     binutils                    

> Accept this solution? [Y/n/q/?] q

So I have 3 questions:

1. Can one install both `binutils:amd64` and `binutils:i386` on the same device?

2. If one can: how? or, what am I doing wrong?

3. If one cannot: why not?

Apologies if this is a FAQ, but

* I saw no answers relating to this (though several similar questions) when DuckDuckGo-ing

* I see nothing @ https://wiki.debian.org/Multiarch/HOWTO indicating that I should not be able to do this.

TIA, Tom Roche <Tom_Roche@pobox.com>