Not directly, as far as I know.
However, you could try to look for an instance that is on Glitch or Hometown, as they allow admins to easily adjust their limits. (Vanilla Mastodon doesn't.)
There are also non-Mastodon Fedi platforms to consider, which tends to have higher character limits too (or no limits at all in some cases).
@FediTips
To clarify, I'm not currently looking for a new instance. But quite a few instances running Mastodon have manually reconfigured the maximum. This one, for example, is 5000.