1) Is there a limit to how many times a contract can be bridged so you do not have a gap in service?
2) How long can a bridge contract be inplace for? (60-90 etc.)
As you've indicated by your research, the authority to extend your contract pursuant to the Option to Extend Services clause has reached its maximum, and can no longer be used on this contract. The use of a sole-source "bridge" contract is a reasonable solution, subject to the written J&A and approval pursuant to FAR 6.304 and agency supplements.
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There is not a standard timeline for how long such a "bridge" contract can remain in effect. However, it should remain in effect for the shortest time possible required to award the follow-on contract. A conservative approach is to award the bridge contract on a one or two month basis. If the bridge needs to be extended, an amendment to the original extension J&A must be approved pursuant to FAR 6.304 (and supplements) before extending the contract. Under this approach, as the bridge contract is extended, the dollar value stated in the bridge contract J&A will increase, which will drive J&A approval to a more senior level. This approach is transparent, keeps the public and other contractors aware of the unique situation, and keeps the award of the follow-on contract as a top priority with the Government team and the senior contracting leaders at the contracting activity.