MPU-5060 interface questions....

I want to know, if using a shift register, and the MPU-5060 accelerometer/Gyro sensor instead of using the I2C interface will work? I want to create a programmed selection of several devices, using a common decoder/demux chip to select the part of my sensors, instead of relying on the I2C. I may not be making sense, but, I want to use several serial inputs, and the others are not I2C usable, as the MPU is. Can I use a SR, to transmit data from the MPU? As well as program it for use? There are methods for my madness, so please be patient, and I will do my best to give more information as you need it, and as I get your questions.

Thanks so very much, group!!!

That is not possible.
The SPI bus is the most simple serial bus. It shifts data.
The UART serial bus does a little more, there is also a start and stop bit and a fixed frequency.
The I2C bus has SDA and SCL and both SDA and SCL signals can go in both directions. It is still a serial bus, but it is more than shifting data.

I assume the sensor is a MPU-6050 ?

It is possible to use other pins with a software I2C library.

Your story doesn't make much sense (to me).
Why can't you use I2C for the MPU-6050 ?

Maybe post a diagram of the Arduino with all the sensors you want to use, and a wiring scheme (length).
Leo..