Typically, they don t like it if you are, because they see the potential for less profit, and typically give you less offers because they don t feel you re worth their time. well someone else is looking for jobs for her too, so she s not worth the trouble you d think it would be the opposite... that they d work harder for your money because they have competition.... naa... these people are lazy by nature and generally don t care about you personally. so... i d answer it with disgretion.. you can say no... and they ll never know.... you can say yes and potentially be shunned... but for what it s worth, my girlfriend uses two temp agencies when she s furloughed from her normal job once a year and they don t seem to mind much...... good luck
check your registrations or agreements. some agencies have no-compete clauses or conflict of interest policies. some may not allow you to work with other agencies at the same time. if you completed a no-compete clause, make sure that it does not extend past your last day of employment, because it may mean that you are not allowed to work for a competitor for a specific period of time, even if you are no longer working with the original agency!