This is supported in Strata.
There is an example in the class
CalibrationZeroRateUsd3OisIrsBsTest which does something equivalent for 3m v 6m basis swaps. Here, the 6m curve (i.e. the one defined as the forward curve for
USD_LIBOR_6M in the
CurveGroupDefinition) uses 3m v 6m basis swap nodes at 1 to 10 year tenors. These nodes are built from the convention
You would want to use the built-in convention
USD_LIBOR_1M_LIBOR_3M instead for the nodes on your 1m curve (i.e. the one defined as being the forward curve for
USD_LIBOR_1M), and just like in the example you will also need a 3m curve in the same curve group for the calibration and pricing to work.
Hope this helps. Let us know if you need any more details.