You certainly can be on several cleared contracts at once. I have several. But those above stated, some companies get possessive. It is always great to have options. If your current clearance is in adjudication, that client may have a higher clearance they are seeking for you, or there is something being questioned and weighed regarding your information. If all other cleared contracts run into the same situation…you will be in limbo there as well. DoD normally doesn’t record a debrief for Secret clearances so you show as “active.” But DoD, in their infinite wisdom allowed many to go far out of scope, and separating military members left without a clearance. And they have no clue until they apply for a cleared position.
My take, if you have not started with company 1 yet…you likely do not have a non compete agreement. I would apply all over, accept what comes your way. If something better comes along you have negotiation power. Company 1 may think high enough and boost their offer or they may rescind. Either way you are getting paid in the here and now. If they do have you sign a non compete agreement…and your clearance isn’t their’s to protect it is yours…they cannot prohibit you doing other cleared work if it doesn’t compete with them. And no they cannot claim all defense contractors are competition. They are…but different contracts are different contracts. Even while on a cleared contract I had ethical companies ask if they could bid my resume, and unethical companies used various older copies of my resume without ever asking me.