No, that's not an option. Not as you've written it.
To repeat, "choosing the Basic Retirement Sum" means
withdrawing funds from your Retirement Account. As cash. Whether you're able to redeposit some or all of those funds into your CPF Ordinary Account is a separate question. Refer to the CPF Board's
"What happens when you reach age 55" page for details.
I don't think we know the Basic Retirement Sum for 2028 yet since it hasn't been announced. For 2027 it'll be $114,100. (The Full Retirement Sum will be $228,200.) If you celebrate your 55th birthday in 2027, and with those SA and OA balances or similar, the CPF Board will sweep $228,200 into your new Retirement Account, mostly or perhaps entirely from SA (after 2026 interest). The remainder will stay in OA. You then have the option (with a property pledge or charge) to withdraw up to $114,100 from your RA in a lump sum.(*) Less if you've made cash top ups to your Special Account.
Since you have the FRS (or nearly so), you can't "choose the BRS" at age 55 without a withdrawal from your RA. It's tautological. If you want to withdraw up to $114,100 from your Retirement Account later, at age 59 for example, you can do that.
What you do with that lump sum cash is up to you, but if you want it to go back into CPF it will be subject to applicable contribution and top up limits.
As I wrote, when you make any lump sum withdrawal from your Retirement Account you permanently reduce the maximum amount you can have in your Retirement Account. The RA limit (the Enhanced Retirement Sum) is computed
inclusive of prior lump sum withdrawals. Maybe this effective reduction in the ERS won't matter in your situation. It depends on how many dollars you want to put in. But it might matter if you want to put a lot of dollars into (or back into) your RA.
It's generally not a good idea to take dollars out of your RA unless you really need them (for urgent needs).(*)
There's that too.
(*) You'll have lots of OA dollars you could withdraw at any time in any increment without touching your RA and without requiring a property pledge or charge. OA earns 2.5% interest, and RA earns 4.0% interest.