'Can I drive it beyond specifications' is a question that comes up frequently.
The answer is 'it depends on what the 'it' is, and what its failure mechanisms are'.
In the case of motors (a shaker is a generalised motor) operating electromagnetically and wound with copper wire, the answer is 'sometimes'.
A motor has several failure modes. The first one to bite kills your motor. Thermal, your windings should not exceed their rated temperature, and must not exceed the insulation decomposition temperature. Mechanical, the force must not exceed the strength of the motor components. Magnetic, the field from your armature must not demagnetise the permanent field magnets.
The output force depends on motor current (for PM motors) so you need an increase in current. For a short enough period, where the windings heat adiabatically (without losing heat to the surroundings), the increase in temperature goes as \$I^2T\$. Double the current, for 1/4 of the time, same heating. If you can identify this constant for your motor, then you can avoid over-temperature by over-driving for only a short time.
Fortunately with shakers and BLDC motors where you have direct access to the windings, and to some extent with brushed motors, you can measure the winding resistance and so estimate temperature. The resistance of copper increases by about 10% for every 25C temperature rise. So you measure room temperature resistance, blast the windings with a short pulse of current, and quickly measure the resistance again.
Unfortunately while that does give you temperature rise, you are still left to guess what the maximum temperature is you can tolerate. What sort of winding insulation did the motor manufacturer use? That tends not to be in the specifications. Would he tell you if you asked him?
If you look at the specifications for your shaker, the 200lbf maximum already says 'intermittent', they've already factored in that the current needed for this is too much to pass continuously. You could use this vague specification as a way to go back to the manufacturer and ask him to clarify 'intermittently' by giving you an \$I^2T\$ value. It's worth a shot.
However, when you come to estimating the mechanical strength of the shaker, or its demagnetisation current, then you're probably on your own. Probe the supplier about these, and he'll know what you're trying to do. His answer will be 'use it within specifications, or the warranty is void'.
When you want to use something beyond its specifications, you take on all responsibility. You could reverse engineer a shaker to see how its built, and estimate strength and demag current. Or you could test one to destruction, and hope that the second one is similar. It might be, or it might not, as long as it meets the original spec, you can't really demand any more of the manufacturer than that.
Or you could just buy the next bigger shaker.