Can a linear motor output multiple and precise linear forces?
You can use a position-based linear actuator like a stepper and a screw thread.
Whether it's a stepper or a servo, it will probably act as a position-control device, that's what linear actuators do.

1) If you want to control the force, measure the force with a force sensor (load cell).

2) Make a control loop to control the force by changing the position of the actuator.

3) Because the linear actuator will move fast and the pressure/ force will rise suddenly with a small movement, put a spring in series with the actuator and load cell.

The spring will make the system "soft" otherwise you'll get big pressure variations as the actuator starts to move.  Here's a graph.


Without a spring the position-force graph is zero, until the actuator hits the back of the syringe, and then rise very fast. With the spring there will be a linear region, the length the spring, before the force steps to infinity.

In the linear region, force will be roughly proportional to position, with an increasing offset as the fluid drains away.

The length of the spring required depends on the speed and accuracy of the control loop. Also, too long will make it hard for the stepper to unload the spring if the flow conditions change, for example.

The spring also gives you an easy way to measure force - just measure the compression of the spring. A load cell does this too, but with a very very stiff spring so it doesn't flex too much.