Based on what I know, I would say that...
'Basandomi' — ba-SAN-do-mi. Stress on the second syllable. Gerund with reflexive pronoun attached.
Use to preface an informed opinion — flagging that your view is based on available knowledge and is thus provisional but grounded. Appropriate for analytical discussions.
'Basandomi su' (basing myself on) is a participial construction using the gerund of 'basarsi' (to base oneself). 'Quello che so' (what I know) limits your claim honestly. 'Direi' is the conditional of 'dire' — 'I would say' — softening the statement.
Per quanto ne sappia, è corretto.
As far as I know, it's correct.
Conditional subjunctive 'sappia' — explicitly acknowledges knowledge limits
Stando ai dati disponibili, sembrerebbe che...
Based on available data, it would seem that...
Evidence-based framing — very precise about the source of your inference
Nei limiti delle mie conoscenze, direi di sì.
Within the limits of my knowledge, I'd say yes.
Formally explicit about knowledge boundaries — academic register
In Italian professional culture, intellectual honesty about the limits of one's knowledge is highly respected. Claiming expertise you don't have is considered a serious social and professional failing. 'Non lo so' (I don't know) said confidently is respected more than false certainty.