Is it possible for Arduino as ISP board to flash an ISP master board?

I have a setup of 2 Arduino Leonardo boards. Let's refer to them as Board A and Board B.

Board A is a master SPI board that is constantly communicating via SPI to an array of sensors. At some point, board A will need to be flashed with a new sketch. That's where Board B comes in.

I want to use Board B go use an Arduino as ISP sketch to go and flash a new sketch onto board A. Problem is that Arduino as ISP uses SPI, which conflicts with the code on board B since board B is a master device communicating to other sensors via SPI.

Is it possible for board B to flash board A via ISP?

note: I'm a noob with Arduino. I found a forum that asked this question, and there were responses with links to other forum pages. I traced through it and... I'm more confused than where I began lol.

Here's a link to the question for reference: