Is it possible to say "as you can"?

Solution 1:

The usual form is: "Doing X as best he or she can."

Solution 2:

"As you can" is a legitimate phrase but it doesn't generally mean "with enthusiasm."

Please send me those reports as you can.

I do not know how pervasive this usage is, but its meaning is, "do this task when you are able" or "when you get some free time, do this task." You could reword it as, "when you can."

The more likely usage would be:

I eat healthy as I can.

This could be reworded as, "I do this whenever I can."

Other phrases that match the particular words "as I can" will be comparative:

I sleep as soundly as I can.

I exercise as often as I can

The last example again is meant to convey frequency, much like "I eat healthy as I can." I suspect that the latter example is a butchering of "as often as I can" and suggest explicitly using "as often."

I cannot think of a specific usage using "can" to suggest someone is doing a task with great enthusiasm. The other suggestions in the answers offer good alternatives with slightly different connotations. More typically, people will use a phrase such as what Hellion listed.

The short answer:

• "As you can" does not imply enthusiasm.
• "As you can" is a valid use
• "As you can" is most likely to imply frequency or timing
• "As you can" is typically used in the form "as [adverb] as you can"