Luton have signed former Peterborough and Brighton striker Craig Mackail-Smith on a two-year deal.
Norwich City have completed the signing of goalkeeper Jake Kean following his release from Blackburn Rovers.
Dyche led Burnley to promotion from the Championship in May despite the Clarets having one of the smallest squads in the second tier.
So far this summer he has added goalkeeper Matt Gilks, midfielders Steven Reid, Matt Taylor and Michael Kightly in addition to forwards Lukas Jutkiewicz and Marvin Sordell - but hopes to boost the numbers further before the end of the window.
He said: "It's a challenge. Some of it is intriguing to know what's out there, what we can do and what we can't do, and it's annoying sometimes because there's things you want to get pushed through and they drag and drag and drag, and we've had that on a few different situations.
"We work hard. I reckon I've made 500 phone calls over the summer to managers to agents to coaches, background on players etc. And that's just me, that's not counting my staff, the recruitment side of things.
"We keep looking and we keep searching for the ones that are appropriate and that can help us to enhance our chances of doing well this year.
"We need more strength in depth but that doesn't just come with anyone, we have to also make sure there's some quality and talent there otherwise it would be counterproductive."
Dyche, who refused to be drawn on reports linking the club with Nottingham Forest midfielder Henri Lansbury, outlined that his scope for potential signings is unmeasurable.
"There's not a definitive number,” he said. “I doubt we'll hit 25 senior players, but we definitely want to enhance the numbers.
"If we had the finance we're spending now in the Championship that would give us a real competitive edge. In the Premier League, we all know what it's like.
"The numbers are vast, even for players who you wouldn't recognise as being market leaders, but they move for very big fees and very big wages. You could get frustrated by it but what's the point? That's not going to get any deals done.
"The only over-lying marker that usually gets any deal done is money, we all know that. We will put good resources into certain areas and certain deals, but there is a limit. The club's future is important, not just the immediate future on the pitch."
Dyche believes his team will be written off before they have started but he is confident they have the right formula to surprise people.
"We were underdogs last year and I think we got used to that," the 43-year-old added.
"It can bring freedom. There'll be an expectation from us, how we perform and how we go about it, but from the outside arguably we'll be deemed probably one of the biggest underdogs there's been in the Premier League for a while.
Watch Burnley take on Chelsea in the first Monday Night Football of the season, live on Sky Sports 1HD on August 18.