When there are more defects with severity 1 and 2, this situation occurs.
As far as I have experienced, there are atleast three projects I faced the same problem and I followed systematic approach as below:
Basic and fundamental Pre-requisite:
Have you got all the test scenarios listed?
-If your answer is YES, then the work is simple (follow step 1). If not, please focus on deriving clear list of TEST SCENARIOS with tools such as Pairwise Testing (Orthogonal Array)

Step 1:
Can we focus on performing REGRESSION TESTS if possible within the
next test cycle?
-Answering YES to this question will help in uncovering complete list of Sev 1 and 2 defects atleast (not the entire defects since full regression tests may not be feasible)
Shortcuts:
Try to implement tools such as CypressIO to automate those tests hence you can extend the same framework to Unit Test (on the left side) and for regression testing/UAT (on right side of testing cycle)
Step 2:
Knowing when to stop testing is crucial. Figure this out in the Test
Plan section 'Suspention Criteria'-do you have a percentage of pass rate accepted and mentioned in
Test Plan?

If this percentage has been provided already,its great, else it has to be amended to make it like atleast 90% of the tests should pass in order to release the software (for example)
If you dont have a test plan , better to write one by following IEEE template at:
https://jmpovedar.files.wordpress.com/2014/03/ieee-829.pdf