If you just mean to install 2 versions of Windows on the same partition than the answer is not really, the Windows folders will be separated, but the other folders will be shared. This will give a lot of access right conflicts because of folder ownerships, I can tell you that much. Separate partitions for each OS where only one OS will be up and running applications at a time will work.
Both running at the same time...if this means that both OS's are up and running applications at your leisure, then you will have to revert to virtualization. Not something you are going to like as it will take quite a bit of steps to do so. Microsoft Hyper-V from Windows Server 2012 (which is free) is likely the most convenient candidate, if you value performance and least amount of Windows licensing problems.
For virtualization it is best to have a "beefy" PC that can handle the load of running both the 32-bit and the 64-bit OS's at the same time with ease. Although you can have impressive specs with laptops, I wouldn't even consider these type of PC's to do this kind of setup. Lots of RAM, fast hard disk(s) and an i7 processor will get you a long way. Maybe an i5 processor will do. In any case, get a processor with lots of L1, L2 and L3 cache, that is more important than the GHz's!
You could also get a spare hard disk of ample size, although I wouldn't use a hard disk of more than 2 TByte as bigger drives could be problematic to boot from (depends on the age of the motherboard and/or what the UEFI BIOS supports). You could divide the new hard disk up in at least 2 partitions and virtualize your 32-bit OS using P2V software packages onto the last partition.
Most P2V software is free, but make sure you select the correct one for either the VMWare Player or VirtualBox software. Converting it later is in most cases still possible, but will take time and success is not guaranteed.
Disconnect the hard disk with the 32-bit OS and start installing the 64-bit OS on the 1st partition. When that is all done, install VMWare Player or VirtualBox in the 64-bit OS and create a new virtual machine using the virtualized 32-bit OS files. If all that went successful you can run applications at your leisure on both OS's at the same time. If the virtualized 32-bit OS works as you expect it to, you can use the original hard disk again for other purposes, you could even add it as a shared drive between both OS's if you want.
Lots of steps, I know. The latter virtualization solution is called tier-2 and most people have not much problems grasping the concept behind it and software to make this kind of virtualizations is freely available. VMWare Player and VirtualBox won't cost you a dime, VMWare Workstation is rather expensive. VMWare vSphere and it's predecessor ESX(i) are similar to Microsoft Hyper-V and also here you have to pay high license fees and make sure you have supported hardware, adding again to the price.
The first virtualization method (with Hyper-V) is called tier-1. Not as simple to grasp for most people, although it is not that hard. Main advantage of tier-1 solutions is the level of performance, which is very close to "bare metal" speeds.
If you have setup your current Windows 32-bit OS in non-standard ways such as lots of partitions, adjusted default folder paths and what not...expect a lot of problems getting it correctly virtualized.
Just making a working backup and doing a complete re-install now sounds about right, does it?
*edited - I should proofread more often