STM32 HAL SPI Remap Single Pin
In general: check the reference manual. Some peripherals can be partially remapped in various different ways; others cannot.

In this specific case: no. Remapping of the SPI3 peripheral is controlled by a single bit in the AFIO mapping register (SPI3_REMAP in AFIO_MAPR); there's no way to do it partially. If possible, you may want to consider using different SPI and/or UART peripherals, or using an I/O expander to reduce the number of peripherals you need. Another option may be to remap the Ethernet peripheral.