Licences do not inhere in code; their obligations attach to recipients through the act of conveyance. So yes, as long as you're the sole rightsholder, you can take code you were distributing under GPLv2 and distribute instead under GPLv3+. You can even distribute it under both licences simultaneously, if you want, though it will be confusing so you probably shouldn't. People who had it under GPLv2 (if any) will continue to use it under those terms, unless they choose to come back and get a new copy under the new terms.
You will be in an odd spot if you accept contributions, since those who had their code under GPLv2 will be obliged to contribute their changes under GPLv2, while those who had it under GPLv3+ will be obliged to contribute under GPLv3 or GPLv3+, depending on which set of terms they chose to have apply to them. It will probably be simplest to get a CLA from contributors that allows you to use their contributions under any combination of GPLv2/3/later you choose.