Can I submit more evidence after already filing a supplemental claim?

Yes. Filing a supplemental claim (VA Form 20-0995) does not close the door on additional evidence. Unlike a Higher-Level Review, where the reviewer generally looks only at the evidence that was in the file at the time the HLR was requested, a supplemental claim is built around the idea that you are presenting new and relevant evidence, and the VA continues to owe you the duty to assist while the claim is pending. You can submit additional new and relevant evidence, such as buddy statements, lay statements, private treatment records, or an independent medical opinion, at any point before a decision is issued on the supplemental claim. The evidence has to meet the "new and relevant" standard under 38 CFR 3.2501, meaning it was not previously considered and relates to an unestablished fact necessary to substantiate the claim. Since your claim already involves a favorable DBQ showing you meet the schedular criteria, additional corroborating evidence such as buddy letters describing how the condition affects your daily functioning, or outside physician notes reinforcing the findings in the DBQ, can only help round out the picture and is unlikely to be seen as duplicative.

Practically, you should send the additional evidence directly to the regional office handling the supplemental claim, referencing your claim number, and you can also upload documents through VA.gov if the claim shows up in your claim status list. There is no formal form required to submit supporting evidence into an open claim; a simple cover letter or a VA Form 21-4138 statement in support of claim can accompany it. Submitting evidence early, before the rating activity begins final review, is always safer than waiting, since once a decision is issued you would need to file a new supplemental claim, a Higher-Level Review, or a Notice of Disagreement to get any additional evidence considered.

If you have buddy statements or outside medical opinions ready, submit them as soon as possible while the supplemental claim is still in the earlier stages of review, rather than waiting to see whether the DBQ alone is enough.